Not a tax person, so please don't sue me, consult your tax adviser.
I BELIEVE, if you take out a mortgage against a rental property, the interest is a direct expense against the income (schedule E). $100,000 rental income-$20,000 interest expense=$80,000 profit (not including other expenses).
If you cash out/refi a house: First of all, I am not even sure it's tax deductible. If it is, there are hurdles before it becomes written off against your income.
On top of that, to give you an intelligent opinion, we would need to see all of the numbers which would be a pro-forma income projection.