Can I go to Cancun, Mexico without a visa if I have an American tourist visa?

Theoretically, you can go to Mexico with an American visa and have to come back within 30 days. It doesn't matter if the visa expires. It can be renewed automatically.

But this is not enough, because generally i-20 will be held for a long time. Maybe you have finished all the classes and i-20 will expire in one year, but in this case, your i-20 can no longer be used to prove your identity! You must have a school report card to prove that you have not completed the credits and will return to school next semester.