The term for what you're describing is known as hidden city ticketing.
Now we'll probably need some more information from you, particularly including the route.
If this is booked as a return then you can't do this because as soon as you miss the MIA-TPA leg the rest of your ticket will be cancelled, and you will likely be left buying a very expensive single ticket to get home (particularly on an international itinerary).
If booked as a single with an international origin:
- you would have to pick up luggage at Miami anyway, so this isn't an issue.
If booked as a single with a USA domestic origin:
- AA would check your luggage through
- they are notorious for tracking hidden city itineraries
- your luggage would likely end up in Tampa anyway because US carriers allow luggage to travel without the passenger, at which point it's really difficult to know what would happen to it until you arrived the next day
Combined, these actions would certainly alert AA. Would they charge you the extra for a first time? Probably not. Could anyone guarantee that, particularly given their need for funds? Nope.
So in short - this probably isn't a good idea.
Have you considered pricing with a <24 hour stopover in Miami? This may not increase the fare much at all.