Does cutting the covering of subwoofer wire affect the sound quality?
Although I'm tempted to state there's some special effect from the insulation capacitance and characteristic impedance that only the golden-ear audiophile can hear (a stunning difference!), no there is no measurable direct effect from that bit of insulation being there or not. The insulation keeps the wire from shorting to the other wire or to ground. 

You can wrap some electrical tape around the bare spot and get on with your life. Heat shrink tubing might be a bit more attractive, but the kind of insulation used for speaker wire is sometimes very low melting point so you might further damage the wire with the heat gun.