Not a problem!
The resistance of a wire is a funciton of cross section area (gauge) and length. In the very worst possible case if each of the individual strands was insulated along its entire length, then you have increased the resistance by 1/number of strands. But in most speaker wire the strands touch and cutting one strand near the end increases the resistance only by resistance of the length of the cut strand.
Using a ten foot length for ease of calcualtion--
Ten feet of 14 AWG has a resistance of 0.025250 Ohms. If your wire has say ten strands then the worst case is that the resistance will increase to 0.028055555555555555555555555555556 Ohms-- less than if you went to 15 AWG.
If only the last inch of one strand is involved then the increase is 0.0002337962962962962962962962962963 Ohms.
Two feet of #14 has a resistance of 0.00505 Ohms!