What do I need to do with a live wire after it's been cut?

You should put a wire nut at the end of the wires, then tape the nuts with electrical tape.

Wire nut:

I would just electrical tape it and then use a tie wrap to hold the tape in place for after the glue on the tape had dry out.

A wire nut is overkill for such a situation in my opinion.

Safety is a precaution, not an overkill.

But by all means, feel free to risk your life.

Anyhow, this is a2k. If you don't use a wire nut, someone is just sure to pounce on it, as if we're talking about 440 three phase.

Wire nuts are known to come off also and to me if anything a tie wrap electrical tape is just as safe in this situation.

Wirenut per Tim very practical approach, Loco, if there's room for it when you reassemble. Otherwise solder:

If you're not familiar with this sort of thing, you'll need a small iron, say 30 w, with a tip about 1/8 in.--3/16 in. dia. BE SURE NOT TO LET 'EM SELL YOU ONE WITH COPPER TIP, which became obsolete 50 years ago in favor of iron; a means for cleaning it, say, charcoal block; and a length of rosin-core solder

Slide on a length of shrink tubing (say, 1/2 in., but just big enough in diameter to accommodate the insulated wire) onto one; strip each, say 1/4 in.

http://www.diystompboxes.com/smfforum/index.php?topic=88735.0;prev_next=next

(I don't like twisting myself, prefer to tin both ends then hold together in parallel fashion [lap] to solder--though requires three hands)

After soldering of course slide tubing over junction and shrink using iron

A hair dryer on high would work better if you are going that route.

Quite right, Bill. My suggestion arises out of laziness