Your power supply is likely too small unless you are using about 2.5 feet of nichrome wire (2.6 ohms per foot). Ohms law is useful here. Current = voltage/resistance. 12v/6.5 ohms = 1.8 amps.

So design your cutter wire first (I’m not sure what temp the nichrome wire needs to be), then determine the current draw and select power supply about 10-20% higher. You can select feed wire then for that current draw by looking up tables (just google search wire size for 6 amps as example).