will the migration assistant remove the files and information from my other Mac?

As posted by @Falk_Gottschalk, no, Migration Assistant does not remove the data from the other Mac.

If you plan to recycle, sell or otherwise rid yourself of the old machine, please have a look at this support doc –

What to do before you sell, give away or recycle your Mac - Apple Support:

https://support.apple.com/en-us/HT201065

No, the old Mac remains untouched.