The purpose of grades is to punish students, something which they are keenly aware of. Remove grades from the equation and hold students back until they have mastered the material and they will cease cheating.

If someone knows 80% of the topics on an exam like the back of their hand and doesn't know the other 20% they shouldn't get a B, they should pass the subjects they know and be asked to retake and relearn the subjects they don't know.

When people know they can make mistakes and the result is not a perpetual black mark on their record (any grade not an A) but they are given the chance to improve and demonstrate this improvement then perhaps they might be more willing to admit and understand mistakes instead of cheating.