When should a Deep finger cut stop bleeding?

If you apply direct pressure to the wound, you should see bleeding stop or slow considerably within 10 minutes, assuming the digit is immobile. Elevate the limb above the level of the heart as well. After 20 minutes, if it's still bleeding, consider calling a doc -- you'll likely need suturing if nothing else. DO NOT TIE A TOURNIQUET EXCEPT AS A VERY LAST RESORT -- Tourniquets are dangerous. You should be able to control almost any bleed in a finger without a tourniquet. Note that if the victim is prescribed aspirin, coumidin, warfarin, or Plavix, you'll see these times increase considerably, as all of these meds delay clotting factors. Even so, 10-20 minutes should control the bleeding.