1. She sucked a mint.

2. She sucked on a mint.
3. She sucked at a mint.

4. Stop sucking your thumb!
5. Stop sucking on your thumb!
6. Stop sucking at your thumb!

7. The baby sucked its mother's breast.
8. The baby sucked at its mother's breast.
9. The baby sucked on its mother's breast.
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Which ones are grammatical?

#s 2, 4, & 8 are the best phrasing. The others are uncommon.