How can I remove this garage sink?

It looks like there are a couple of valves at the bottom of each faucet handle.  (See pic, at arrows)  If these turn off the water, you should have very little spillage.   Turn the valves as far as possible and then see if twisting the faucet gives any water.  (Have a bucket handy just in case)  If these valves do what I think they do, you should be able to just remove the faucet handles and be done!  

hopefully you have a valve on each of those lines.  Those valves on the elbow going into the Faucet are useless.   theres no way to untread them without disconnecting them from water line.

Best thing to do would be turn water off which my be the main valve.   I'd cut the pipe around that corner an put caps on it.  Then removing rest of sink will be easy.  

turn the supply valves off before removing it.  if you can't find them, or they're unmovable, then you have to shut down the water to the garage [or house] and remove the sink -- after which you replace dead valves or cap the resulting pipes.  --grampa