Backyard mint too grassy
While it is true that there are a variety of mints, I think your biggest challenge is that it is "late in the season."  I find that here (Philly, USA), in August, all of my herbs tend to develop a bitterness that is not there in spring and early summer.  While it may be the variety, I don't think it is the age of the plant, as my mint comes back each year as well.  It seems that the "soft" herbs are just past their prime now.  My rosemary and sage are fine, thyme is ok, but softer herbs like basil and lovage have a higher bitter component.  Try your mint again in the spring.

Another thought: Pulsing into a paste my also bring out flavor components that are not desirable.  What about steeping the leaves in the milk and cream (this would work if you are making a custard based ice cream and heating the cream), then straining them out?