Flow drill stab
Two partners both partners face each other with knife in regular (earth) grip, blade forward, and edge down. Start at slow speed, but try to keep the speed the same throughout the drill first partner stabs at throat, receiver turns with deflection and mirror image stabs at throat of attacker. Make sure you control the opponent’s knife hand/arm throughout the counterattack to prevent counter slash. First attacker evades with deflection and attacks low, inside knee/hamstring/ femoral artery (a little anatomy is very helpful in knife fighting) attacker again mirrors attack at same level. Again, counter attacker must control knife arm throughout counterattack. Repeat this flow for bilateral high and low targets. Throat, femoral, brachial, eyes, groin, lung, etc is a good kind of target migration. Also, practice with both right and left hand holds, more reps with your weak hand than you’re strong. It will help with both ambidexterity and balance/footwork.
Notice that the attacker is not trying to control the counter attackers arm, only to attack. The counterattacked is doing the controlling, and the drill assumes the counter attack "fails". However, you are practicing following that attack back to the source after deflecting/avoiding the attack and preventing counter slashes that would follow the stabs normally. Pay attention to the distancing, too. You want to be close enough to draw the stab, but still be able to evade and follow it back and counter, keeping the flow going. Obviously, the attacker gets to be counterattaker in the next round. The attacker is learning to target and to attack with as little telegraph as possible, but without overt feints. Don't start depending on feints and other cheap tricks until much later in your training. Feints, stutter steps, pseudoshifts, arm, leg and shoulder fakes are all great to learn, but you must learn good balance, distancing, targeting and footwork first. For every trick, there is a counter, and a well-trained knifer will read your fakes.
Good technique is good technique, period. Once you are moving smoothly in both the stabs and the counter stabs, add some unbalancing to your counter, but not grappling or throws, you just want to learn to unbalance subtly, so the attacker starts attacking from an unbalanced position and makes more mistakes. Pay attention to the little things here. Also you can start incrementally increasing the speed of the attacks and counters, start trying to simultaneously mirror the attack. By the time you start doing this, you are (should be) used to seeing stabs coming in from various angles, noticed how your foot placement affects how the attacker targets, and should be able to read the incoming attack. The key is to get smooth and to be able to flow into and through several exchanges of attack/counter/attack/counter, etc in an unbroken flow. You will be surprised at how fast things move once you get your distancing and footwork down.
Finally, once you get good at single attack counter, start with both partners countering. That is, attack, counter; counter the counter (keeping control of the arm through the counter and counter counter, etc) gradually increasing speed and try to get as many exchanges as possible. This is not easy to do correctly, which is why you won't get many exchanges at first. You should be able to see the similarity of this drill to kihon Nagare. Oh, yeah, reminder, move in a triangle.
Cutting drill 1
Targeting - arm, wrist both partners face each other knives in earth grip. Attacker starts with angle 1 attack (see first drill for definition of angles) defender steps outside angle and upward cuts wrist of attackers arm, right into angle 1 attack to attacker, who has evaded the wrist cut and now fades to outside angle to evade slash, counter to angle 2, wrist cut and counter slash to angle 2 by defender, etc. start slow and focus on timing the counter slash to wrist with the cut, keeping same speed throughout drill, notice that the drill becomes very difficult to flow with if your footwork isn't right. Attacker does not do wrist slashes, only bodyline attacks. The focus of this drill for attacker is to be able to retreat from a committed attack and evade a counter, then flow right back into a counter. The defender is working on accurate angle of cut and accurate targeting on a moving target (attackers wrist.) This drill gets pretty fast and complicated, but if you keep the speed controlled and the techs clean, the flow training and distancing practice is great. After you are comfortable with the basic flow, add arm presses, unbalancing, and random angles of attack. Note that the defender has to automatically recognize the angle of attack coming in and mirror it.
Cutting drill 2
One partner stands in fighting crouch, blindfolded second partner moves to a position on a circle around the crouched fighter. He/she steps in and touches the first (blindfolded) fighter, who tries to spin to that position and touch the attacker before he/she can step away. The touché can lunge in the direction of the touch to reach further, too. Always step straight back, no cheating. Return to front and repeat. Works on both footwork and directional skills/ proprioception. Speed per se isn't the issue so much as moving efficiently. You will be surprised at how many times people fall down doing this. (Works on Ukemi, l too, I guess:-), also they stand up then turn, etc. the most efficient way to move is to spin around the spine with the hips. Also, most people turn one way easier than the other. It takes a bit of practice to do this, especially blindfolded, for some reason, ad it is a lot tougher to do than it sounds, but it is a fun drill, and it works well on balance and footwork/ Oh, yeah, the second guy works on moving quietly:-)