If you use a lot of mint, certainly worth sorting out those 2 containers. Coming to the end of their leafing stage now but cutting back, splitting, possibly discarding some roots to give the best ones a chance to grow. Watering and a decent mulch should see you OK for next year.
I would, yes. Cut back, take them out, find a good rooted piece, and pot it back up. Discard the rest - compost it, giveaway little rooted plants, whatever. It'll probably give you more leaves this autumn until it gets really cold. Then trim it back and it'll shoot again in spring and be nice and bushy.
“It's still magic even if you know how it's done.”
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Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.