Mentally Not Over Ex?

Means: I'm trying to work this out in my head, emotionally, get over it; think about the breakup and figure out what happened; fall out of love with my ex.

I would say it depends on the nature of the person who has said that.

If that person has a very structured, or habit based mind, then it may simply mean they are still trying to get over all the habits that he/she developed with her/him, or over the way of thinking he/she developed with her/him etc.

Or it could be that the person fixates easily (said in a better way 'quickly focuses, but takes a long time to defocus')

Then there's the chance they he/she was quite hurt by the break up, and is jaded/cynical, and knows it - and because they 'know' it, they express the emotional issues as a cognitive/mentally issue.

But if it isn't any of those (or something similar to those), then there's a good chance that when they say 'mentally', they mean 'emotionally', without wanting to say 'emotionally'