On the App:
Swiping left on a message will delete your messages with that person. Or if you tap on More you can Block or Report the profile to stop communication.
Click on the 3 dots on the top right of the conversation, then click Block, this will will un-match you with that profile and delete your messages with that person.
There is no limit to the number of people a member can block. If you change your mind you can go to the Blocked Profiles section of your settings to unblock a member and start communicating to them again.