'Would you mind + verb-ing...' and 'do you mind + verb-ing...' are used at the the beginning of a polite question/request structure, while 'if you don't mind' can be used at the beginning or the end of a phrase, and are more like a tag, meaning that we do not use it as an indirect request in all cases. Examples: Request: If you don't mind, could you come in early tomorrow? If you don't mind, could you shut the window? Statement/order: I need you in early tomorrow, if you don't mind. It's cold in here; shut the window, if you don't mind.