Possible. Not cheap. Not easy.
Audio compact cassette data recording is still possible, but has not been commonly used in a quarter-century or so. To record on that format, you'll need to scrounge both hardware and software, much of which you'll either need to scrounge or write for yourself. Basically, you'll be learning a whole lot about digital to analog signal processing, and of course analog to digital processing, and about hooking all of this to an audio port or (maybe) to USB.
DAT (technically DDS) cartridge tapes are available for USB and various other I/O buses — based on a quick look, maybe US$900 or so for the drive, plus the cost of the cartridges — and those will require some OS X software that can access the USB device to record your backups. Used drives are cheaper. The command-line tar tool might work here, depending on how successfully the USB interface works. I don't know of any, off-hand. DAT (DDS) reliability isn't all that great — the cartridges aren't quite single use, but they don't last very long. This format has been retired, and newer generations of this format will not be available.
Next step up is DLT/SDLT/Ultrium/LTO, and those too are available — more expensive than DDS — and you'll need some add-on software for recording to those cartridges, commercial or maybe tar or possibly some open-source. The current-generation Ultrium/LTO devices are still fairly common in mid- and high-end computing, but are comparatively rare on OS X systems. ATTO has some options here.
There are some other tape formats and media.
Scrounging an old USB floppy drive will probably be easier, if this is computing nostalgia as might be inferred. Those are still available from various sources, and very inexpensive. Going price for these is US$10 to US$15 or so, plus the cost of the floppies.