I filled my taxes on april 13th and got accepted. payment of taxes was dated for april 13 using direct debit. but today is april 15 and taxes are not debited yet

It takes a few days for the IRS and/or your state to process your return and draft the payment from your account. 

April 13 was a Saturday. Your direct debit would be processed today Monay and may take up to three business days to hit your account.