The sentence you wrote is almost correct but needs a small change to fix the grammar. Here's the corrected sentence:
"Deer grow their antlers in spring and lose them in autumn."
Explanation:
- You don't need a comma before the period at the end.
- The sentence is a simple fact, so it should end with a period (full stop).
If you want, you can also add "every year" to make it clearer:
"Deer grow their antlers in spring and lose them in autumn every year."
This sentence tells us that deer grow their antlers in the spring and then lose them in the autumn, which happens annually.