I’m pretty sure this was an episode from some sort of anthology series in the very late ’60s or early ’70s. The gist is a near future time where food is strictly rationed, each family has a card which they use to get their allotment. The card for the family in the story is damaged somehow so that it will not work in the food dispenser.
The father is unsuccessful navigating the bureaucracy of the time and ultimately cuts off his arm to feed his family so they can make it to the end of the month. The episode closes with a shot of him, suit sleeve pinned up to indicate the missing arm.
I thought this was an episode of the Paulist TV series, Insight. (Which, by the way, someone really needs to put on the Internet for free because it was — and probably still is — amazing.)
A TV movie called And Then They Forgot God.
And Then They Forgot God (1971)
Prolific episodic television writer Sy Salkowitz wrote and directed this outré dramatic telefilm set in a dystopian future. With a grim plot twist that rivals the darkest of Twilight Zone episodes, this humanistic parable centers on an average couple (Joseph Campanella and Beverly Garland) as they face starvation due to a Kafkaesque bureaucracy. Also features Adam West as a policy-obsessed prosecutor.
I’d like to see that again. It scared the hell out of me back when it aired.