In dictionary,
"would" is used to ask somebody politely to do something
Ex: Would you mind leaving us alone for a few minutes?
However, I think that explanation is so simple or it does not explain clearly.
"would" make your sentence more hesitative since it is giving a hypothesis.
And to make a sentence more polite with "would", we have to look at the real meaning of a sentence.
Ex: "Do you mind if I use your cellphone?" (the listener doesn't have to hesitate to mind it, the listener is welcome to mind it, it makes the question less forceful & therefore is more polite) is more polite than "Would you mind if I use your cellphone?" (the listener hesitates to mind it, it makes the question more forceful & therefore is less polite)
But "Would you mind leaving us alone for a few minutes?" (the listener hesitates to mind it, it makes the question less forceful & therefore is more polite) is more polite than "Do you mind leaving us alone for a few minutes?" (the listener doesn't have to hesitate to mind it, the listener is welcome to mind it, it makes the question more forceful & therefore is less polite)
"Do you mind if I use your cellphone" or "Would you mind if I use your cellphone"? Which one is more polite?
Best Answer
"Would" is more polite. "Do you mind" means the action is already underway and you're asking the person if that bothers them. "Would you mind" asks about a hypothetical situation that hasn't happened yet.
Note, though, that neither form actually asks to borrow the phone. Technically, they just take a survey. It's common for a wise guy to stand there and say, "No, I don't mind", and not offer their phone. "Could I please borrow your cellphone?" would be more likely to avoid that.