In this case, you would know that a neuter noun had been mentioned before, precisely because of the 'mit'. If it were a common noun, it would be 'min'. In fact, you only ever use possessive pronouns with something that is known or has already been mentioned, otherwise you'd use a possessive adjective plus a noun.
Of course, if you're translating from English, either would be fine, since you don't know the context.
To be quite honest, I am not 100 % sure why I do what I do when I speak my own language (Swedish), so I learn Danish here to see if I understand Swedish better - that's the mystery with 'native language'. To rephrase what I said above: you say: "Det er mit" or "Den er min" so it refers to the implied noun. Probably that's it. Though 'Det' feels more neutral, like English 'it'.