Bmx bike lever?

how do i connected the back brake wire to the lever?

does it involve cutting anything?

No,not to connect the cable,but after your done perhaps.
Place the bike upside down and then pull the lever towards the bar as if you were braking.You should see the hole and slot for the cable end to fit into.
It is best to put the end in then insert the end of the cable into the cable housing .You might want to take the housing out of the lever as well to ensure it is in right.This is also a good time to oil the cable and then pull it into the cable housing as all lubrication is good on a cable.

If there were any cutting at all,it would be after the cable has been fitted,oiled and then secured to the brake caliper.The excess cable might be too long.
Normal cutting devices usually do not work too well unless they are both hardened steel and damned sharp.
If you cut the end of the cable shorter make sure to wind the cable again so the braid is in flow with the rest of the cable.
A frayed cable end can really be a problem and can hurt as it is sharp and coil like..
If you do not have the actual aluminum cable end to seal the end of the newly cut cable then solder can be used.You can also use glues and tapes but if the end is not bent and kept away from scraping a kicking you will regret it.
I hope this can help.