Can a graduate program rescind my offer if I don't complete a previously declared Minor? I am a physics major and had declared a 'Minor in Computer Science (Expected)' on my US graduate school (PhD) applications. I have been accepted by a couple of programs but I am currently still one course short of completing the number of required courses for the minor. I am currently enrolled in this last course (a theoretical Computer Science course) in my current (last) semester. The course is not very relevant to the programs I have applied to (Physics and Data Science) -- more 'relevant'/applied courses that I have an interest in were unavailable. The course is quite time consuming and is affecting my performance in other courses I am enrolled in (physics graduate electives and statistics). I would very much like to withdraw the course, however, if I do so, I would only have completed 4 of the 5 required CSE courses counting toward a minor and will not get a minor.

I am concerned about how the graduate program I decide to attend will view this. My ultimate worry, of course, is whether my acceptance could actually be rescinded for not having completed the minor. (I have still completed 16 of the 20 required credits, so I still have courses in Computer Science, I would just not receive this tag of a 'Minor in CSE'.)
I...declared a 'Minor in Computer Science (Expected)' on my US graduate school (PhD) applications. I have been accepted by a couple of programs...[C]ould [acceptance] be rescinded for not [achieving that qualification].


It depends on the offer. If an offer is conditional on the basis of you achieving a minor, then, yes, that offer can be rescinded. Otherwise (the offer is unconditional), it cannot. (Conditionality of an offer may be buried in the fine print.) Albeit, we're in legal territory and INAL.

For practical purposes, I suggest that you contact the universities that have made offers and discuss your situation with them.