Can I replace a 3-gear crankset with a 2-gear one cheaply and efficiently?
On MTB you don't get such thing as 2-chainring cranksets. Cranksets come in parts: cranks, bottom bracket and chainrings. 

If you are buying crankset separately, chainrings are not included. This is to provide a better flexibility in chainring selection: different materials, shapes and tooth numbers. On cheap cranksets you can not separate chainrings, and in this case you'll need to replace the whole assembly. So one of your options would be to check if your crankset allows to remove the granny ring. If you have chainring bolts there, you are in luck: take the granny ring off and adjust the front mech.

If your chainrings are moulded into the crankset, you'll have to replace the crankset, and that might be not a simple business. In this case it's quite likely that you have square taper bottom bracket and these days it is not easy to find a descent crankset for square taper. So you'll have to replace the bottom bracket as well... and this can be a world of cash spent just for removing a granny ring. Not really worth it, unless you want a better quality/lighter cranks.