Agramunt had come under fire for a visit to war-torn Syria in March during which he met al-Assad.
The move came after the parliamentary assembly of the human rights-focused organisation voted to amend its procedures to allow it to dismiss its president or vice president.
There was previously no procedure for sacking or withdrawing confidence from the assembly’s president.
His visit came weeks after a UN commission of inquiry into the conflict concluded that al-Assad’s regime had committed multiple war crimes during last year’s battle for Aleppo.
This include the deployment of poisonous chlorine gas and airstrikes on civilian targets.