Transfer from iMac 2015 2 TB HDD to Mac Mini M4 Pro 512 GB SSD

You can not split up your data to different drives during the initial migration.

carefully read > Transfer to a new Mac with Migration Assistant - Apple Support

If it all will not fit in the new Mac?

Then you need to reduce the data on the old Mac and make a new backup for migration.

To do that you can move your Photos, Music, Movie Libraries to an external hard drive.

Move your Photos library to save space on your Mac - Apple Support

Change where your music files are stored on Mac - Apple Support

Move your iMovie for Mac library - Apple Support

If you go that route, it is best to have several external drives on hand.

one to move your Photos, Music, Movie Libraries into.

one to backup the Photos, Music, Movie Libraries on the first.

one to backup the reduced down old Mac to use for migration to the new Mac.

+1 on den.thed's assessment. In short you cannot migrate (using Setup Assistant OR Migration Assistant) because both are an all or nothing proposition on the data migrated. The only way you can do this is by manually moving large libraries from the old Mac to external storage on the new Mac and then telling the apps that use those libraries where the libraries are located.

What you were attempting to do is save money which you can do however it is a LOT more work to go this route. If you are willing to do the work then okay. If not then the wise thing to do is return the MM and buy one with adequate storage so you can migrate easily.

What den.thed and rkaufmann87 told you was basically an expanded version of what I said I did as a solution (the link I provided was actually to something rkaufmann87 posted a while ago, but apparently that was not found to be useful). If you're going to be using a smaller internal drive, as it appears you are saying, then shrink your current internal so you can then use Migration Assistant or Setup Assistant to just migrate the smaller drive. As I said, I shrank my old boot drive to about 850GB of stuff on a 1 TB drive to 150 GB by offloading my big space eaters and then just used Setup Assistant. Yes, it took me about a day but most of that time was away from the computer waiting for files to copy.

Others are advising you to buy a larger internal drive which is fine, but realize that a 2TB drive will cost an additional $600. You may even be considering upgrading to a 4TB drive which would cost an additional $1,200. When talking about that scale of price difference it wouldn't surprise me if people went with an external drive (I could buy a lot of 4TB external drives for what a 4TB internal would cost--but maybe you're made of money). A mini is, after all, a desktop model so we aren't talking a lot of inconvenience the way we would be if this was a notebook.

I had to do similar. I don't know if this was the best way but I committed to permanently using an external drive for my "data" on the new system. I copied data type files (e.g., music, videos, photos, some other) to my external drive (and its backup) and trimmed my old 1TB boot drive down to a size where its contents would fit on the new internal drive (I actually got it way down to about 150GB). That allowed me to just do a simple migration.

You may find the tips in this thread to be useful transferring files from a 2008 iMac to a … - Apple Community

If you are anything like me you will have a load of rubbish that you haven't looked at for years and probably will never need.

Take this opportunity to get rid of it.