After buying a thrift store bike with a lock permanently attached to the seat, I set out to cut the lock and cable off. This proved to be a difficult endeavor. The lock was a Masterlock key-type, the kind that locks fenses and industrial doors. So that wasn't coming off. Cutting the cables was the answer, seeing as it was the thin braided type in a black plastic sleeve. The braided steel cable was about 1/4 of an inch thick, pretty thin. Seems easy, right?

Tools attempted:
wire cutters (small)
hacksaw (large)
industrial strength bolt cutters (large, 2 foot arms on each, blades were dull from cutting tree branches so I sharpened them with a knife stone and they still wouldn't cut through )

The final tool attempted worked. A dremel tool with a small 1/4 inch circular grinder/saw attachment, used at the end of the cable where I pulled the plastic sleeve back. The saw sent up sparks three inches in the air each time it made contact with the cable. After a couple minutes of gingerly cutting at each side of the cable, it finally gave way.

If you ever see some dirtbag hovering over your bike with sparks arching up like he's welding, he aint welding. He's stealing your bike. A battery powered version would do the trick, but it's going to take a couple minutes to complete. If it was a cable any thicker than 1/2 an inch, forget it, I can't picture a way you can cut it. So good news to those of us with good locks and cables