Meaning trap
put down
euthanize an animal
To kill an animal painlessly, usually because it is very ill or suffering, often as a humane decision.

Don't mix these meanings
Same phrase, different job.
To kill an animal painlessly, usually because it is very ill or suffering, often as a humane decision.
'put down' also has the more basic meaning 'to place something on a surface'; this is the advanced sense.
Hear it in context
Notice where the phrase sounds natural.
After years of illness, they finally had to put their dog down.
Some people argue that it is more humane to put down animals that are in severe pain rather than prolonging their suffering.
Fix the pattern
One small grammar move makes it sound right.
Not: We had to put down our dog to sleep.
Say: We had to have our dog put down. / ...put to sleep.
Don't blend the two idioms — it's 'put down' OR 'put to sleep', not 'put down to sleep'.
Which sounds natural?
Tap the one a native speaker would say.
'Put down' is the gentle everyday term for euthanising a pet; 'administer euthanasia' is clinical.
Build natural chunks
Words that usually travel with it.
have/put + animal + down
- the dog put down
- the cat down
- a horse down
- humanely
Don't confuse it
Related
Other meanings and phrases to compare.
- put down (to place something on a surface) — 'put down' also has the more basic meaning 'to place something on a surface'; this is the advanced sense.