A problem that is quite likely to occur with just grabbing a precompiled binary (e.g., from Debian's mipsel) is the mismatch of needed libraries needed by the binary and the libraries that your system has available.
In particular, in Debian, we try as much to have everything dynamically linked, which means that the library versions are important (to be more specific, the libraries SONAME should be the same, for the binary to work).
You can try to determine which libraries are available in your system and their version an see if there is any version of mkvtoolnix that uses something close by a sort of binary search with Debian's snapshot archive.
If you don't succeed in that, then you may want to cross-compile mkvtoolnix yourself and my preferred solution to that would be to use debootstrap with qemu's userland emulation to create your "semi-native" mipsel environment.
Then, you can proceed to compile the programs in a regular way (it will make your life easier if you use try to grab Debian's source for the packages that you want and use, for example, debuild).
And, to be 100% sure that you won't have problems with libraries, you can statically link your mkvtoolnix binary, to make it as self contained as possible.
