price to replace ipad mini port

If it's under warranty and deemed to be a manufacturer's defect then it could be free.

If not, they don't really replace parts as you pay the out of warranty price to exchange your broken iPad for a refurbished replacement.

iPad Service Answer Center - Apple Support

Depending on the model, year of manufacture, and if there is (or not) an AppleCare+ plan involved, the price may vary. An Apple Store genius or product specialist, or an Authorized Apple Service Provider could inspect the unit and offer advice and/or prices based on other criteria that is missing from your initial inquiry here.

Because these usually have ports affixed to the logic or main circuit board, it may better to consider costs to replace the iPad, unless the unit is relatively new.

{PS: the link provided in above reply, which wasn't there before I started mine, is a good place to start.}