OP's construction is extremely "non-standard". Many instances in the first page of results from Google Books for "would you mind to" are language guides citing it as an example of incorrect usage, and several others appear to be from non-native speakers anyway.
I don't think there's any grammatical rule in play here - there's no fundamental difference between mind and, for example, care. And we certainly say "Would you care to do that?" - although in the negative, native speakers invariably prefer "Would you mind not doing that?" rather than "Would you care not to do that?" (but you could use wish there without raising eyebrows).
Perhaps because it's a construction primarily used in "polite/formal" requests, native speakers may be extra careful to take note of and replicate the exact form used by others. Which makes the "idiomatic preference" particularly strong in this case.
EDIT: I don't know why all this answer has collected so far is a downvote. I admit this example...
I should not mind to die for them, my own dear downs, my comrades true.
But that great heart of Bethlehem, he died for men he never knew.
...is effectively "doggerel", but I don't think it would have been published at all if it had been considered blatantly ungrammatical.