As a teaching-assistant, how can I avoid repetitive teaching?
An answer looking at the bigger picture:

Stop teaching the same class all the time!

If you've taught the same class so often that you can reuse your material without thinking about it much, then it's time to branch out next semester and teach something else.  Teaching a variety of classes is more fun and rewarding (as they say, the best way to learn a subject is to teach it, so this way you learn more subjects).  It is valuable experience for an academic or teaching career, and showing a breadth of teaching experience can be helpful in a job search.

Maybe your department just keeps assigning you this course and you assume you have no choice.  Try just asking to be assigned something else - contact whoever is in charge of those assignments and ask what else might be available.  Of course you might not get what you want, since making teaching assignments is always complicated and requires many constraints to be satisfied, but there's a good chance of having your preferences at least taken into account.  If you don't get what you want this semester, you might have a better chance in a future semester as they try to make it up to you.