There is no way how MKV multimedia files could be converted to SSA subtitles. However, you can simply export subtitles from existing MKV files and save them in one of the suitable formats like the SSA.
Convert Matroska multimedia container to SubStation Alpha subtitle file.
We found 4 software records in the database related to .mkv to .ssa file format conversion.
Microsoft Windows software - convert mkv to ssa on Windows
A Matroska extraction utility
Convert from mkv file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned mkv to ssa. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
A program for working with Matroska MKV files
Apple macOS / Mac OS X software - convert mkv to ssa on OS X
A Mac version of the video editing suite for Matroska
Linux/Unix software - convert mkv to ssa on Linux
A set of utilities for handling Matroska files in version for Linux