Q: Would a mini split heat pump help to dehumidify a basement?

A: A mini-split heat pump head (i.e., the part that is inside the house or basement) WILL dehumidify the air inside the house but only when it is operating in AC mode i.e., during the summer months. Since basements are generally cooler than the rest of the house, it may not be operating as an AC unit very often and so it may not actually be dehumidifying the basement much at all. In the winter, when it is operating as heater it will not be dehumidifying the basement air. 

How effective this is for you is going to depend on what the source for the humidity is in your basement. If the humidity comes in summer (which is quite common because warm humid air enters the house and then condenses on surfaces in the basement because the basement is colder than the rest of the house), then the heat pump will dehumidify the basement air but only when it is in AC mode, which as I mentioned it probably is not doing very often even in summer. However, if the source of humidity in your basement is due to rising damp, i.e., from a high-water table or from rainwater leaking in from the soil then this tends to happen in winter when the ground water is highest or we get rain on top of thick snow. In winter the heat pump will be heating your basement. So now you will have warm humid air in the basement. Warm air rises. Humid air rises. Warm humid air really rises. When this warm humid air contacts a cold roof surface it will condense. This will lead to mold and rot. This is a common problem in cathedral ceilings. Because of this, I think relying on a mini-split heat pump to dehumidify your basement is not a good idea. I think you will be much better off installing a heat-pump hot water tank. These dehumidify the basement air whenever they are heating the hot water, which is year round. Heat-pump hot-water tanks are much cheaper to run than fossil-fuel hot-water heaters. The dehumidification comes as a side benefit, but in my opinion, it is a major benefit. If you don’t want a heat-pump hot-water tank, then just getting a dehumidifier will probably do the job. Dehumidifiers provide a small amount of heat in the basement too.