Welcome to iMore! It sounds like you need to turn off the snooze function on your alarm.
1. Open Clock app
2. Tap on EDIT, then tap on the alarm you wish to edit

3. Make sure SNOOZE is toggled off on your alarm

This should fix your problem. Keep in mind, it's possible to turn keep the alarm from going off again even with snooze enabled but you need to swipe right when the alarm sounds. If you just tap on it you're activating snooze at that point. If you have no need for the snooze function, just keep it off like I do.