Most countries will consider a damaged passport invalid and require it to be replaced.
For instance, the United States says:
If your passport has been significantly damaged, especially the book cover or the page displaying your personal data and photo, you will need to apply for a new passport. Conditions that may constitute damage requiring you to replace your passport include water damage, a significant tear, unofficial markings on the data page, missing visa pages (torn out), a hole punch, or other injuries.
You will need to obtain a replacement passport.
But if there are still valid visas in your existing passport, you should keep it, and contact the consulates of those countries for further information after you obtain the new passport, as your old visas may still be valid even in the damaged passport, or they may require you to transfer them to the new passport.