My first thought was Edward VIII back in 1936, and that was because he abdicated the throne.

Diana lost the HRH title, and I think at least some of her patronages, in 1996 when the divorce went through (and she died in 1997.)

Harry and Megs just recently, supposedly by their own request.

There have been other minor royals who have been taken down, but Andrew is the biggest one in recent times for sure (and his was for an actual crime, not simply through quitting or getting divorced.)