Is it possible to hop on and off on Hurtigruten?

The ferry is used as a means of local transport although when i travelled on it a couple of years ago most passengers seemed to be tourists making a cruise for several days. If you get off you are unlikely to get on the same ship unless you travel fairly rapidly up the coast so I do not think you will get the same cabin.

I'm pretty sure that your plan would be possible and your cabin would still be waiting when you board the ship again in the next harbor. Hurtigruten warns explicitly that you will have to get to the next harbor yourself and that this will be quite expensive when you miss the ships departure. And it will depart, with or without you. They regularly have to deal with passengers who miss the departure by accident, so why should they handle people who do it on purpose any different.

But you should keep one thing in mind: on large parts of the coast the ship is the fastest way to travel. I once took the night train from Trondheim to Bodø, boarding the ship there because it was not viable to reach Trondheim by plane before the ship departed. In this case we overtook the ship that had already left in Trondheim on its way to Bodø. But (and that is a big "but" with capital letters) this is the only train route that more or less follows the coast in Norway.

If you really want to go to the next harbor by yourself you will have to look into renting a car one way (and I wouldn't expect to find a rental agency in small harbors) or pay a lot for a taxi. Busses an such will have to go around fjords and stick to their schedule, so I wouldn't count on them either. If you decide to go with a rental car keep in mind that you will have to go around fjords as well, or depend on ferries to shorten the route over a fjord. And don't underestimate the weather, especially in the north, and especially in winter.