Can I dissolve mint in water and drink it?

No, mint won't dissolve in water (leaves are mostly cellulose), but it does make excellent tea.

Boiling water, steep 5-6 minutes.

For best results, I recommending purchasing whole leaf mint intended for use as a tea. That way you can experiment and determine which kind of mint you feel makes the best tea (or make your own blend, I like spearmint tea with a single peppermint leaf thrown in).

Mint leaves, and plant matter in general, won’t dissolve in water no matter how finely you grind them. They are largely made of substances which are simply not (very) soluble in water. At best you’ll achieve a “suspension”, where the particles remain suspended in the liquid for some time; but it won’t be stable, and eventually they’ll sink to the bottom or rise to the top.

If you want to make mint tea, strain the leaves out once it’s brewed.

You have several options for mint-flavored water, and none of them includes dissolving dried mint leaves in it. As others said, leaves don't dissolve in water (plants would be in a lot of trouble if they did!)

1. You can make a mint tea. You pour hot water over the dried (or fresh) leaves, leave it for a few minutes, then strain it. Buying mint tea in bulk will be cheaper than buying it as seasoning, but make sure you buy the mint you want - teas are more commonly peppermint, while seasoning is more commonly spearmint.
2. You can place whole fresh mint leaves in a water carafe, then drink the water throughout the day.
3. You can buy mint essential oil and drop it into water. Be very careful with dosing here, the ratio is in the range of a drop or two per liter, or even less. The taste will be quite different from using dry leaves, but you might find out you like it.
4. You can buy commercial mint flavoring and dissolve it in water. The taste will be close to the essential oil, but easier to dose.
5. You can buy candy with a strong mint flavor and dissolve it in water. The taste will be again very close to the flavoring, but it could be easier to find the candy than the flavoring, and if you find out you don't like it that way, you can still eat the candy, while you will have less use for a bottle of mint essence.
6. You can buy commercial mint syrup (will contain sugar and coloring in addition to the flavoring) and dissolve it in water. The taste will again be close to the essential oil.
7. You can keep simply drinking the combination of dry leaves and water (or, if you prefer, pass it through any kind of mill you want, such as a spice mill or a coffee mill). It won't dissolve and you will have to drink the leaves along, but there is no harm in that. The taste will be different than mint tea - it won't be as "cooked", but it will also be much weaker.
8. You could theoretically look into making your own non-water infusions and extractions. This is mostly an enthusiast's niche.

For ordering the alternatives, I used a rough combination of taste, convenience and sensibility. You might find that your preferences differ, and that you are happiest with something that is not at the top of the list.

In pure water, no plant matter will actually dissolve. You can get close by forming a suspension (this is how green tea made using matcha is made, as well as hot cocoa), but it will not actually dissolve because cellulose and lignin are very insoluble in water and account for a majority (by mass) of all plant matter.

There are three other methods used instead to produce beverages, sauces, and other water-based liquid derivatives from plant matter:

• Decoction: This is the process used to make true ‘Turkish’ coffee, and consists of making a paste out of the plant matter and then boiling that. It tends to be the best option for extracting things that don’t dissolve well in water but dissolve well in oil or fat, and is also better than infusion or percolation at extracting things from roots, bark, and other woody plant parts, but is also the most actively involved of the three processes.
• Infusion: This is the process used to make most teas, traditional maté, and traditional western-style coffee, as well as being the main process used to extract essential oils. It consists of simply putting the plant matter in water (or alcohol, or oil, depending on the type of infusion) for an extended period of time and letting stuff leech out through diffusion. Infusion can be done hot or cold, and in the context of teas is often referred to as ‘brewing’. This is the easiest method in general, as it requires very little supervision when done hot (just make sure it doesn’t boil over or end up with too little liquid) and essentially no supervision when done cold. The flip side is that it takes longer than decoction for an otherwise roughly equivalent strength preparation.
• Percolation: This is the process used to make modern western-style coffee, and consists of preparing the plant matter in some way to make the compounds you care about more soluble in water (for example, roasting and then grinding the coffee beans for western-style coffee), and then pouring (usually boiling) water over the result into another container. This method is best used to control the concentration of things in the resulting mixture as the resultant concentration is largely just a function of the volume of water, volume of plant matter, and temperature of the water, unlike infusion or decoction where the total time taken also impacts the concentration. Repeated percolation can be used to get higher concentrations easily as well. This tends to work best with stuff that can be ground down into a coarse powder (like coffee beans or cinnamon bark).

For most plants in the mint family (not just Mentha species, but also stuff like balm, sage, catnip, and rosemary), decoction and infusion both work reasonably well, and all three need very hot water to be practical because most of the compounds that you actually want for flavoring or medicinal properties are not very soluble in water. Most preparations you will find for mint are likely to be infusions, though they may not be water based (infusing mint into ethanol for example is very easy, because menthol and the other flavorants found in mint are all very soluble in ethanol, and is part of how mint-flavored liqueurs were traditionally made). Note that dried versus fresh mint will give you different flavor profiles for otherwise identical preparations.

You can, of course, also just grind up the mint and create a suspension (just like with matcha or hot cocoa), though you will generally want dried mint for that. Fresh mint will give you a paste instead, and while that can be used to create a suspension, it will usually be a lot stronger in terms of flavor.

You can grind dried mint in any blender or food processor. You don't need a particularily good blender, as long as the mint is dry enough you should end up with something similar to Matcha Tea, maybe a bit more coarse.

If you're not happy with the result you can use a mortar and pestle to make the powder finer, but be aware that it is a time-consuming process.

As the other answers already explained the powdered mint would not dissolve; however if mixed vigorously (as you'd do for matcha) it will take much less time to steep.

The beverage will also have a different (most likely stronger) flavour and texture due to the mint leaf particles in suspension.

Whether the faster steep time is worth drinking a "chunky" tea (or the hassle of filtering the tea through a coffe filter) is up to you.

Leave the mint tea in a ultrasonic bath overnight and most of the mint will be pulverized into the liquid. Add some soy lecithin as a emulsifier depending on how oily/waxy the mint plant is.

Though I never tried this with mint, it works well with green tea and comes out like a matcha tea hybrid.

Yes, you can, the water wil taste kind of minty then because the flavor of the mint is strained into the water.