The value of the mortgage has nothing to do with taxes due, the tax is on the income, less certain deductions. As a non-Irish domiciled landlord, your tenants would be obliged to send 20% of the rent to Revenue on your behalf.
Try doing a search on here, there are many similar threads.
As a non-Irish
resident landlord. Domicile is a complex legal concept and is irrelevant in this situation.
I live in the UK too, but my tenants never withheld any tax from rent. I know they are supposed to, as otherwise they are liable for it in the event that I don't pay it. However, I have always paid the tax, so the tenants never bothered.
A few years ago the Revenue made a complete mess of my tax return, charging me an astronomical amount of tax. When contacted about it, they sorted it out but (presumably to show that the boot is on their foot anyway, no matter what mess they make) they then send me a letter, saying that my tenants must withhold these 20% and pay it to the Revenue, and that the demand for that had been sent to the tenants.
I replied saying that I had always paid all the tax due, so don't see why they should demand this tax from my tenants, as the correct tax gets paid anyway - by me, rather than the tenants. That it wasn't easy for me to find the tenants and if the tenants are put under pressure by the Revenue with this, they are likely to leave, and then neither I nor the Revenue will get anything
The Revenue didn't reply to me. Whether they sent anything to the tenants or not, I don't know but the tenants didn't start deducting any tax and still don't. I pay the tax to the Revenue, as before, and everybody seems to be happy