Sillcock Replacement
That sillcock appears to be soldered on to the water pipe. There should have been a female adapter soldered on to the water pipe and then the sillcock would just screw onto the water pipe. You've got a few options here:

1) Cut the water pipe, solder a female adapter on the water pipe and screw in a new sillcock.

2) Cut the water pipe and get a SharkBite sillcock and shove it onto the water pipe.

3)Unsolder the existing sillcock, clean up the water pipe and solder a new sillcock onto the water pipe.

I would be doing the first option as it makes future replacements easier.