General synonyms:
* Imitate
* Copy
* Reproduce
* Emulate
* Mock (can have a negative connotation)
* Parody (implies humorous imitation)
More specific synonyms:
* Aping (for closely imitating someone's actions or mannerisms)
* Echoing (for reproducing sounds)
* Mirroring (for reflecting someone's behavior or emotions)
* Simulating (for creating a realistic imitation)
The best synonym to use will depend on the specific situation and the nuance you want to convey.