Will doing too many yoga poses hurt you?

It is certainly possible to injure yourself by doing yoga asanas incorrectly, including over-doing past your limit.
I say incorrectly because part of proper asana practice is developing and exercising self-awareness. Yoga is not at all competetive, and while you want to do the best asana that’s possible for you and your body in the moment, that never means pushing beyond a limit where you’ll get hurt.

There are several “styles” of yoga these days that encourage pushing yourself and being competitive. They are not true to the classical intention and practice of yoga asana.

The general mantra is…listen to your body.

Yoga is a practice, a tool. It can be used for good or as a weapon against yourself, just like meditation, aerobics, weightlifting, fasting, etc.