Some of the exercises are very hard. That is expected. But it depends on how deep you want your learning to be. If you are happy enough with a superficial understanding, then just read the solutions.
But if you want "operational" knowledge. The knowledge of how to put all of that to use and to extend it in your work, then you need to do a lot of the exercises. Mark them off when you succeed and come back to the ones you can't do later on. Or, find someone more knowledgeable than yourself, who also understands learning, who can give you minimal hints when you get stuck.
The issue is in the way the brain works. Long term memory works not by seeing something once and having it immediately imprinted somehow, but through rewiring of the neurons through repetition, reinforcement, and feedback. If you don't do that, you won't develop a deep understanding - or even memory of what you've seen.
But, since many of them are hard, and there may still be a few research problems hidden in there, don't work until you get frustrated. But instead of giving up and reading the solution, put it aside and go on to another. Come back to the hard ones occasionally and see if you can do better.
The more you do, the more it will enable you to do others, even if it doesn't make them easy.
In some books the exercises are what give it value. If you can do them, you have some deep knowledge TAOCP is like that.
But the same is true of the books you have for your coursework in CS and in Math.