There is a pretty easy fix for horse cutting corners. It begins, as the resolution of all problems begins, on the walk. The gait is the slowest and easiest gait to control on a horse, and is where all training begins. Practice riding your horse through the arena, walking him around corners to a point where he has almost no room before allowing him to turn; at the same time, apply the leg that is facing the center of the arena (inside leg) behind the strap firmly. This tells the horse that it is not allowed to cut corners. Do this at each corner of the arena you reach, each time you firmly apply the inside leg; thus telling the horse that it has no choice but to come to the corner. You’ll want to do this in both directions, which will teach the horse to always stay on the edge of the arena when riding into a corner; Also, praise him every time he walks around the corner without fighting your aids, this will really reinforce his good behavior and his desire to please you.
Once you’ve got him going really well around corners at a walk using those cues, and you feel confident he’s doing it right, try him out at a trot. That way you can tell if you’re ready to listen at a faster pace. If the horse continues to listen to the aids, reward him with praise and give him softer signals. If you choose to ignore his prompts, take him for a walk and resume the exercise as you walk, strongly signaling him with your inside leg behind the cinch and bringing him almost to the corner. This tells him that in order not to have the aids applied roughly, he should come to the corner. Once he is obeying you again, try jogging again. Anytime he doesn’t listen at a faster pace and starts cutting corners again, get him back on the trail and use his cues hard.
As he becomes more accommodating and listens to the trot, you can lighten his assists: use your softer legs and give him more slack to allow him to get through the corner without cutting it off. He will tell you that his good behavior made you trust him and he will be happy to oblige. Trust him, but if he reverts to the old behavior of taking shortcuts, immediately fix the problem by walking him back and pushing him into corners. He will eventually learn that in order to move at a faster pace he has to reach corners smoothly and avoid lurching into the center of the arena.