Carlos, without going too much into detail and the semantics of it, here are the basics.
1) Assume the objective of the operation was to a) extract 5 kidney stone and thus b) reduce the inflammation of the kidneys
2) Assume that you have only managed to c) extract 4 out of 5 stones or d) all 5 but the kidney are still inflated
3) This means that you have achieved PART of your objective a and b. Alternatively, only PART of the operation worked (extracting stones) but the other part (reducing inflammation) did not work
4) I would not say that MINOR is entirely incorrect. But generally, Minor implies "insignificant" and Success implies "great/grand/significant", so in combination they are awkward.
Finally, as a doctor, you have to be as precise in communication with patients as possible. Partial success means some things have worked and others have not, so you can have a discussion on that. Minor success is vague and confusing.
Peace