I think you have a compression valve on the bottom. That maybe leaked, and somebody put a special connector line in place that had a built in valve on its input to compensate.
I am thinking that I would inspect that copper pipe, an if it was in good shape, I might cut that pipe shorter. Then onto that pipe I would put either a new compression valve or a Sharkbite valve.
Alternatively, you could not cut the pipe, and try removing the bottom valve, but leave the nut and ferrule. See if the new valve will screw on and use the old nut and ferrule. If it will not, you either get a ferrule puller, or you cut and dress the pipe.