Not quite sure what you mean by "autosaves"
Are you talking about the backup files?
For a non-workshared project, those are the ones with .0001.rvt.....0015.rvt names
For a workshared (Central) project, all the "backups" are stored in a folder by the same name as the Central file, with a "_backup" suffix.
If that's what yo're referring to, in either case, the answer to your question is No. Both the .000x.rvt file and the _backup folder are in the same location as the Revit file. No options there.
BUT... You can set the NUMBER of backups that are saved.
When you do a SaveAs, click on the Options button. The number of backups is set there.
The default # of backups is set in whichever Template file yo're using

Yes

That is my problem. The backups get sent to the deleted items folder on google drive, which take up space and require regular purging. Which isn't crazy difficult, but annoying.

CTC's Family Tools has a Delete Backup Files. Don't know if the paid part of that runs on a consistent basis. Dynamo could do the same thing for you.

If you wanted it automated, you would have to start looking into the Revit API to go delete on a consistent basis. Or write some PowerShell, or some Batch File.

Plenty of options.

So set your # of backups to 1

Thank-you to everyone for the responses. I think my issue can't be fixed through revit atm(it would be great if they let me choose a destination for them) and is instead a Google file stream issue. I like the rate of backup files from revit and find having them there refreshing. I have enough space on my computer to save all the recovery files and would prefer to keep them all, but not enough space to keep them in the cloud.

The problem for me is the deleted ones, not the active ones. I had to delete ~2000 of them from google drives recycle bin and again, I want to keep these files as a backup, just in a different location.

My current plan moving forward is to save all files to the cloud, NOT delete any backups automatically, and then cut and paste them into a separate backup folder periodically. That way the cloud is constantly backing the important up to date files and I only have to spend a minute or two a week dealing with this problem. (google drive is tedious to go through and delete the deleted items as they load slowly..)

cheers.

If these are not workshared files why not just copy them to your computer and then copy them back when you are done?