IANAL, but in this context, it means "disposed of," or "abolished," probably based on some usage involving "throwing [something] in the trash can," just like one might say something was "binned" in the UK.

It can also mean "fired (from a job)," as in "Donny showed up to work drunk, so he got canned."

It's a somewhat informal "discarded."

During the Vietnam era, several people used the 1st Amendment to avoid getting drafted. To quote Wikipedia, "United States v. Seeger, 1965, ruled that a person can claim conscientious objector status based on religious study and conviction that has a similar position in that person's life to the belief in God, without a concrete belief in God.[4] United States v. Welsh, five years later, ruled that a conscientious objector need have no religious belief at all." Widespread opposition to the draft during the Vietnam era led to official termination of the draft system in 1973. Since 1980, adult males are again required to register for military service in case their country enters a state of war. But there is no real punishment for failing to sign up, and the country hasn't officially been at war since 1945.

Edit: sorry I can't get the quote to work and it's late at night here. This'll have to do.