As with empty hand fighting, to neutralize the opponent as quickly as possible, you must strike the best targets. This does not mean you always need attempt to strike vital points. Opponents will usually be defending their vital areas making these areas hard to hit. Since drawing the first blood has such a tremendous psychological advantage, the more you strike your opponent the better, regardless of where you hit. A primary target is the weapon-wielding hand. By disabling the hand that holds the weapon, you neutralize the weapon.
Unless you regularly train in knife fighting techniques, your best option is to fight in the same manner in which you normally train, except you will have a knife in your leading hand to add to your arsenal of weapons. Use the leading hand in the same manner you would if it did not have a knife in it. Use the knife to block, jab, hook, uppercut, etc. If opponent has a knife, always be aware of it and its location.
Contact fighters are used to getting hit. Many times, they do not bother to block because they know they can take the attack and come back with an even more powerful attack of their own. When the opponent has a knife, this is not an option. Point fighters, especially ippon (one point) fighters, lose if the opponent scores one technique on them, so they are trained to avoid or block every attack. Theoretically, a point fighter would have a better chance than a contact fighter of surviving a knife attack (when neither is a trained knife fighter).