I'm using my 64MB mini on FullHD display quite nicely (Ambient on enhanced mode, other screens not), but 32MB mini isn't really that suitable for it.

If you want to use enhanced display, you can reduce graphics memory usage by changing DisplayEngine settings in MorphOS preferences. Don't allow double or triple buffering (remove checkmarks on them) and you get a single buffered mode, which still contains all the eyecandy, but consumes much less memory. Although you might see little tearing when moving things. You'll need to reboot or switch some screens when switching those settings.

Another option is to use a 16bit screenmode. Play around which combination will be best for your usage (single buffering or 16bit or both).