I think there is a difference. Mock, belittle, disparage, disrespect, put you down, diss: these are all things I can do to make you seem less worthy than you are. Diminish, in the sense Donne uses it, means you actually become less worthy.
"For all his greatness however, he was diminished by his last years and by Churchill's disastrous decision to recall him to the Admiralty soon after the outbreak of the First World War. " - book review on Amazon
"He was able to handle Martinez with ease — yes, he was diminished, but no, that didn't stop..." - article discussing whether a boxer is likely to win his next contest.
These quotes use "diminish" to mean "become less". It is harder to find uses where it means "to make less", and where the subject and object are both persons ("I would never diminish you"). In none of these examples is someone diminished merely because of what people say about them.