Mautino said the bill "accidentally makes felons of tens of thousands of Illinois citizens" who already own a military-style weapon.
The amendments were approved with Democratic votes only.
Republicans refused to cast votes. GOP Rep. Dennis Reboletti of Elmhurst said Madigan's procedure puts politics before public safety.
"Why do we continue to play these games of going amendment by amendment?" Reboletti said.
Republicans have strongly opposed Madigan's new floor-debate style. He has also used his "weekly order of business" process to discuss concealed carry and pension proposals, and Republicans also refused to vote on pension amendments Thursday.
Halfway through Tuesday's debate, someone on the Republican sided shouted, "Stop the circus!"
Tuesday's amendments also called for forcing individuals who would be exempted from the ban, such as members of the armed forces and jail wardens, to store their guns with a locking device that renders them inoperable or under a key or combination lock.