Belt on A/C Pump Going

If I throw the belt around the A/C pump, will that cause any problems for the rest of the car? Can I run the car with out it? My A/C does not work anyway right now. Inspecting the belts the other day I saw a piece missing on that belt. Belt looks a little frayed as well.

just snip that belt off youll gain hp a bit anyway nothing extreme youll just sweat your nuts off if you dont have t tops and also snip the smog pump belt off to gain some more quick hp