How to replace a compression valve behind sink?
That valve uses a compression fitting to attach to the copper pipe. Here are your options (in order from easiest to hardest which is also, conversely, in opposite order from a reliability standpoint), I will label them as to each method's reliability. All three methods require you to shut off the water supply:


Buy an identical valve and screw it to the nut that is already trapped on the pipe by the compression ferrule. Remove the existing valve by holding the valve body with one wrench, then unscrewing the compression nut with a 2nd wrench. When you screw the new valve onto the old nut, reverse the procedure above and know that you will have to get it nice and tight for a good seal. (good)
Cut behind the existing nut and ferrule (you will likely need to use a hacksaw because there does not appear to be room for a tubing cutter). Use a "sharkbite" style push-on connector with 1/2" male iron pipe threads (MIP/NPT). Thread on the appropriate replacement valve. (better)
Cut behind the existing nut and ferrule (you will likely need to use a hacksaw because there does not appear to be room for a tubing cutter). Solder on a male adapter with 1/2" male iron pipe threads (MIP/NPT). Thread on the appropriate replacement valve. (best)