I am running LMDE with MATE on a 64-bit system, fully up to date.
As far as I know, all other file types launch the correct app.
I tried uninstalling (ie. purging) audacity, but MATE now launches Libre-Office!
After re-installing Audacity, PDFs launch Audacity again!
I also tried purging and re-installing evince, but same behaviour.
I cannot find a way to configure which app is launched when a file is selected. It seems that this would be the proper way to fix this.
The only other possibly relevant fact I can point identify, is a problem during the last system upgrade. Prior to the upgrade I was happily running LMDE with Cinnamon, but after the upgrade completed, Cinnamon always fails to start. So I simply switched to MATE and it has been working fine - that is, until now.