Andrew Smith is a 3rd-degree BJJ black belt based out of Richmond, VA (Revolution BJJ). He runs BJJ Path, a video tutorial website.
Counters to Counters
Fundamental jiu jitsu techniques tend to yield equally fundamental defenses. One of the very first defenses you will likely encounter to a knee cut guard pass (based on fundamental guard maintenance principles) is the scissor or knee shield. This means that you can no longer move forward with your knee cut as before and will need to make some adjustments. What follows are three different "counters to the counters," so to speak. You can determine which works best for you, or you can take a look at the specific situations under which approach might work best. Remember: advanced techniques are really nothing more than fundamental techniques layered on top of one another.
Running Into the Shield
When you run into the knee/shin shield, one simple approach is to stop moving forward and instead thread your arm through, weaving around their top leg but in front of their bottom leg. This helps to keep their legs pinched together (I prefer to punch the ground, but others will sometimes grab the bottom pants leg). If your right hand is punching through, grab their (same side) collar with your left hand. This will help you close the distance, and also help to keep them flat. Seal the deal by driving your head into their far shoulder, ensuring that they will flatten out. From here, you may simply be able to sprawl your leg free, or you can use a "yogafoot" approach. Be sure to flatten them completely as you finish the guard pass.
When the shin slides in front during the knee cut here, sometimes a slightly different angle is just the thing to do. Here, make sure your grip on the lapel is higher up, so that you can slide your elbow down and back (to block their hip from following you). It is imperative that you control the sleeve now, so that you can pull your partner's arm way up. Once again, the name of the game is to flatten your partner's shoulders. Next up, your hips need to face the ceiling. This is likely the most nonintuitive part of the move; this isn't the typical way a knee cut pass works, but it can be extremely effective in finishing the pass under these circumstances. As you turn your hips back over, you should be able to snag a Kimura grip and have some fun.
Another very simple approach involves an even more subtle angle change. Start with the same pre-existing conditions: you are cutting the knee across, and your partner catches the shield before you can move any further forward. In this strategy, you simply want to drop your elbow, as before (recall that this makes it tough for them to follow you with their legs any further up), and then just turn your hips downward. This allows you to disconnect from their legs, making sure that their hips remain pinned under your ribcage and hip area. Focus on keeping their knees pinched together, and then seek out the sleeve to finish.
Once you get all three of these options down, one will likely become your favorite. This will likely frustrate many of your partners for a while, until one comes up with a good way to counter what you're doing, and then you'll be back to the drawing board. Always remember that advanced techniques in jiu jitsu arise in exactly this manner, and you may well be helping to encourage innovation at your gym when you use this layered approach to problem solving. Don't despair, but instead remember that you are adding to the overall body of BJJ knowledge out there! It is growing quickly. As always, let me know how these techniques work out for you.