There is no way how MKV multimedia files could be converted to ASS subtitles. However, you can simply export subtitles from existing MKV files and save them in one of the suitable formats like the ASS.
Convert Matroska multimedia container to Advanced SubStation Alpha subtitles.
We have found 4 software records in our database eligible for .mkv to .ass file format conversion.
Microsoft Windows software - convert mkv to ass 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 ass. 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 ass on OS X
A Mac version of the video editing suite for Matroska
Linux/Unix software - convert mkv to ass on Linux
A set of utilities for handling Matroska files in version for Linux