Is it permissible to consider the remaining amount of a debt as Zakat, and deduct it from the Zakat amount that must be paid to the poor?

It is not permissible to waive a debt owed by a debtor and count it as Zakat, because Zakat involves giving and taking, and waiving a debt is not like that. However, the needy person can be given Zakat to pay off his debt.