Is one absolved of responsibility when donating to charity the amount owed to the state as tax, after the concerned authority refused to collect it? And is tax evasion permissible according to Islamic law?

Evading taxes is an offshoot of the ruling on their imposition. If they are among those that are permissible to impose and collect, then they must be paid. Otherwise, nothing is binding upon you. If they are binding upon you and you are unable to deliver them, then give charity on their behalf. However, if you give charity on your own behalf, and not on behalf of the entitled party, then your responsibility is not discharged by that, due to the lack of benefit to the rightful owners. Sheikh Ibn Uthaymeen was very strict on this matter, considering giving charity on one's own behalf in this situation a sin that does not discharge one's responsibility.