I bought a new faucet for the kitchen sink and was preparing to install it. I can shut off the cold water valve, but when I tried to shut off the hot water valve the knob turns but it almost feels like it might be stripped, so it doesn't turn off the water. I'm wondering if I can basically take off the knob to the hot water valve and then use a wrench to turn off the valve without shutting off the main water supply to the house. I can't really tell if it's just the knob that needs to be replaced or the shut off valve itself. Any help would be appreciated! :-)

If you think that knob is turning and the stem is not turning yes you can remove the knob and turn the stem to shut off the water but this will be a temporary fix.
The best way is to shut off the main water supply to the house remove the angle valve and replace it with a new one they are very cheap see the Image below, Thanks.

John