1. To say somthing about somebody or somthing in a negative way sometimes in a joke, also known as a cut down.
I cant believe she put him down like that.
A good put down is, your mom is like a racecar, she burns 4 rubbers in one night.
To kill an animal 'humanly' because they are too old or too ill.
We are also totally bullshitting ourselves when we say "There's nothing we can do", "It's in too much pain", or "It'll be better off this way", especially since humans in the same conditions go to nursing homes, hostpitals, get a private nurse, wheel chairs, a ton of meds, and no one ever says "There's nothing we can do, we have to put down Grandma."
Grandpa: The dog's fourteen, and he can't move around anymore, we gotta get him put down.
Grandchild: But why, Grandpa?
Grandpa: Blame the society, not the executioner, sweetie.