This question applies equally to savings and mortgages.
Your mortgage is borrowed in Euro, the bank will have borrowed it from European Banks in Euros.
If Ireland left the Euro, I'd assume the European banks would still want to get repaid in Euro's. Hence our lender would also want to get repaid in Euro's from the borrower. Otherwise they would make a massive loss on the loan.
I queried this some months ago with RaboDirect in regard to savings, if Ireland left the Euro, would my savings be converted to Punt Nua or left in Euro, and i got a reply along the lines of "The bank will adhere to whatever leglislation is enacted at the time, in the unlikely event that it will happen". You can take from that, what you like!