"Should I just clip off the stems at the ground and let the plant develop new tops?"

I would give it a shearing just above the first pair of leaves. The mint will grow back bushier. I routinely do this throughout the year when I want to harvest some.

"If I cut off the tops, is it OK to make tea with it, aphids and all, or should I discard it?"

That's your choice. I doubt the aphids would be of concern if ingested. I personally wouldn't just because of the "ick" factor not because of a safety issue.

Rodney

LOL! Thanks Rodney. Making tea includingt the aphids does have an "ick" factor but I hate to just toss the tops...and I figure boiling them will also keep the aphids from crawling off and infecting something else.

Is it typical for spearmint to be more resistant to aphids? I like it better anyway.

Potted plants, especially indoor ones, are prone to different problems than ground planted plants. Out in the gardens, lady bugs and other bug eaters will keep aphids under control most of the time. Plants indoors or in patio settings don't always have the same "hunters" patrolling them, eating the aphids. Wind, rain, and sun can also help keep some pest numbers under control versus house grown plants.

FataMorgana

Here is my most affected pot, a mixture of peppermint and spearmint. I recently split it so it hasn't filled out yet. The spearmint has a few aphids but not like the peppermit.

I'm also getting some aphids in nearby pots. Maybe I need to bring some ladybug larvae in.

This peppermint is doing great in the ground. As FataMorgana said, it is drier here and more exposed to the sun...and lots of exposure to areas with aphid-loving bugs!

Wow you have many mints!

Also look for ants. Ants have a bad habit of "farming" aphids, kinda like cows (nothing against cows), for the heneydew the aphids leave behind. The ants will raise and hatch the aphids and then carry them up to a good place to feed. You could reduce or eliminate part of the aphid problem by dealing with ants - and they'll sometimes set up living quarters in pots where you are growing mints.