Why does my car wheel hop when the tires spin
Because that's what happens when the tires spin. If you're wanting to stop it from happening don't dump the clutch. If you're wanting a tuner type car change the struts, sway bars and get race style lower control arm bushings and sway bar bushings.
It's common for front wheel drives do this. Under acceleration, the weight transfers to the rear leaving the front end light creating the "wheel hop".