Cuts on the inner forearm
The trouble with using a knife as a torture device is that unless the torturer is very skilled at what he does and knows anatomy very well, he's as likely to kill as extract information. In this particular case, there are two decent sized arteries running along the inside of the forearm, the radial and ulnar arteries (see photo). Stabbing down into the flesh and dragging the blade toward the wrist is almost sure to hit at least one of them.
Slashed wrists is a common method of attempted suicide which is widely known to not be terribly effective because by the time the artery gets to the wrist, it's pretty small. It can take hours to bleed to death from a slashed wrist, but cut the artery higher up the arm and you've got bigger problems. Shock can set in pretty quickly - my best guess being within ten minutes. And after that, you've got some time to stabilize the victim, but he's not going to be doing much to help you as he will likely be unconscious or too confused to function.
If your victim gets away within minutes of the cut and applies pressure directly to the wound and then gets help, chances are good with surgery and perhaps blood transfusions that the victim will live.
If you want a lot of pain, an alarming amount of blood but not truly immediately dangerous, you could go with any major muscle group that isn't near a major artery. Muscle bleeds a lot. Some locations that are pretty choice, the calf muscle, the muscles of the outer forearm, the top of the thigh or outer thigh area, the shoulder. Think meaty parts that aren't near pulse-points. The muscle will likely stop working for a while, but with some stitches will generally heal up pretty well.
Alternately, cuts that bleed an alarming amount, hurt a lot, and are generally unlikely to cause death are cuts to the ears, scalp or forehead. Try not freaking out when someone slashes you across the forehead and there's blood running into your eyes.
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