There are many problems.
If it's a manned mission, you'd need to supply a multi year mission
If it's unmanned, then you'd be in trouble if anything breaks
In either case, you'd need to bring propellants along to bring the stuff back
If you manage to get the stuff back, then you'd have to de-orbit it.
The only way it would be in any way, shape, or form feasible would be to use the minerals in orbit (or at least not on Earth). There's no reason to go out to the asteroid belt to get what you can get for pennies on the dollar here on Earth.
If you're interested, one book you may want to check out is
this. It's the book which helped me decide that I wanted to go into aerospace. It has sections on the feasibility of asteroid mining, along with many other extra-terrestrial resources (Water from Mars or its moons, Helium from the Jovian planets, etc.)