The hard drive in my Mac Mini G4 is in a rough shape, so I plan to replace it with an mSATA SSD. The HDD contains both Mac OS and MorphOS partitions, and I'd like to retain this arrangement. What would be my best option to clone the contents of whole disk? Is this something can can be done while the HDD is still in the machine, e.g. with a PPC Linux Live CD?

I'm not sure if there are any special tricks to consider with SSD drives (like not writing to all cells which would happen when writing a whole image into it), but in theory it should work by making an image of the whole disk either with dd in Linux, RAWDISK: in MorphOS, or with similar solution.

Here's some documentation if you want to do it by booting from the MorphOS installation media (use the RegisterISO first, as a tip) http://library.morph.zone/Creating_Backups#Cloning_a_Partition_or_Hard_Disk_as_an_Image_File

Thanks, I wasn't aware of the RAWDISK method in MorphOS. That looks like the most convenient since I'll need a fresh installation disc anyway. Since it clones the whole disk I assume I won't need to do any blessings to make things bootable on the new drive.

I don't remember how those "blessings" work in this kind of situation... are they stored on the filesystem or in nvram? If in the filesystem, it shouldn't be an issue, but if in nvram or such, maybe it still would work if the partition setup is similar? Unless it stores more info about hd somewhere... but at least for MorphOS part it's easily fixable with HFSSetMacBoot if it becomes an issue.

"blessing" is only needed on the filesystem level, so if you do an exact/raw copy, it won't be needed again.

This turned out to be a bigger ordeal than expected. The external HDD I wanted to put the backup image on is NTFS formatted, which is read only when booting from the live CD. Since the I'm trying to backup an 80GB disk, my only 1st party option seems to be ext2/3 according to this list:
https://library.morph.zone/Filesystems
I tried Linux Live CDs too that come with ntfs-3g, but both Ubuntu 16.04 and Ubuntu 16.10 froze on me after a while. I could move the cursor but the desktop would be unresponsive.
I thought about trying a MacOSX install disc, but it has the same issue with NTFS.

I have a 2 TB external USB drive formatted to Ext2/3 (can't remember for sure was it 2 or 3, but shouldn't make difference). The Ext filesystem doesn't auto-mount on MorphOS, but I get it easily mounted with the Mounter tool.

I have successfully made backup images of my 240 GB Mac mini and 256 GB PowerBook drives on it under MorphOS using the RAWDISK: device.

So, my suggestion is that you should sacrifice original formatting on some external HDD and format it to Ext2/3. Then it should work in both MorphOS and Linux just fine. I did partition and format my drive under a Linux machine to be sure it'd end up as compatible as possible, but I guess it could be possible under MorphOS too, although I don't remember if I've ever tried it.

Or if you have an ExFAT formatted drive, maybe it could be used somehow? At least on Linux, but maybe on MorphOS too if you create a modified ISO image where you have inserted needed files for the filesystem (and keyfile) and boot from that? :)

After rummaging through storage I finally found an old 1.5TB SATA drive with an USB enclosure. I haven't used it in years because it has a bunch of weak sectors, but fortunately I was able to reformat it to Ext3. This should work as a backup drive.

I typically just clone my drives from a to b instead of messing around with a filesystem target but it depends on what you want to do with the backup. I just need a way to recover things once things go downhill.

I'd have done that too, but I have no IDE to USB adapter, and I didn't really want to buy another gadget I'll use maybe once. Fortunately the ext3 formatted drive worked, now I can make snapshots of my ailing hard drive to another one when necessary.