How to disconnect this silver connector to my plumbing?

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Aren't you lucky, you've got a job insurance combination angle stop and hose.

Shut the water off, disconnect the angle stop/hose combo and replace with a 1/4 turn angle stop and separate hose to the appliance.
It is a crimp connection. You can't disconnect it unless you saw it off.
Could be that the shut-off is threaded onto the pipe (kinda hard to tell from here, but base of shut-off sure seems rather large). In that case, you would first disconnect the hose at the other end, then unscrew the shut-off.
These are made/sold by FLOW TITE and there are several U-TUBE'S;