According to this halachic ruling: “A debtor who has insufficient means to pay back his debts should not donate more than one third of a shekel (per year) to charity until he completed the repayment of his debts.” …someone who has a mortgage should seemingly be exempt from ma’aser kesafim (or at a minimum give one third of a shekel per year) until he has paid back the mortgage loan -?-
The cited halachic ruling refers to debts whose repayment is not arranged, and which have to be paid back on a immediate basis. Earned income must be first of all dedicated to paying back the debt (which is an immediate obligation), and this obligation defers the maaser contribution.
A mortgage does not obligated immediate payment, and is paid back in installments over many years. Earned income does not need to be dedicated towards the mortgage repayment, because this is arranged over the years.
Therefore, somebody with a mortgage is obligated in maaser like anyone else.