Deleting music files from two different Apple Computers

You need to delete from two libraries if the files are locally downloaded to both libraries. If the files are in the cloud for one library and downloaded to the other then you can remove items from the library where they are downloaded and they will disappear from the other, otherwise yes, you need to delete from both computers. Having deleted from one computer the files that were deleted will show on the other computer with a cloud status of removed. See If songs are missing from your music library after you turn on Sync Library - Apple Support and the section Check the cloud status of songs on your Mac or PC.

A smart playlist with the rules Match music for the following rules, Cloud Status is Removed to quickly reveal all removed items in a library, so that they can be quickly selected and deleted without needing to manually duplicate the specific removals on the second machine.

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iCloud Music Library which is part of Apple Music or iTunes Match is designed to keep multiple libraries and devices in sync. Changes to metadata including artwork should sync automatically from one to the other. Deletions are mirrored immediately on iOS devices, and for any tracks that are only in the cloud, but downloaded items in a computer library are marked as removed, giving you an opportunity to add them back to the library if you deleted in them in error. If you're actually wanting to remove those items you can create a smart playlist to show all removed items so that you can quickly select and delete from the second computer.

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You're welcome. 🙂

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