As I happen to enjoy both Unix and the Atari ST(E), I prepared some ready to use SD card images containing Minix 1.5 at http://subsole.org/minix_on_the_atari_st
You can't do that much with the OS a part learning C and Unix, and it's text mode, but it's fun to see it booting. And after all the first Linux version was developped from a Minix 1.5 system on PC , so you know what to do next
NB: concerning the names: Minix is the name of the OS from which Mint took one part, the filesystem. A part from that they are rwo different beasts.