DYSMANTLE doesn't have it's own integrated co-op network at the moment unfortunately.
However, you can play with 2 player co-op anyway by using Steam Remote Play "Together" (intended by the devs).

Explanation/Guide:

https://steamproxy.net/steamstore/remoteplay

It boils down to:

1. Launch Dysmantle
   
2. Press Shift + Tab
   
3. Go to your friends lists (go online there if you have set your online status to offline) and invite the friend you want to play with.
   
4. The friends has to accept the invite
   
5. You can play!

Steam Remote Play will allow you to invite someone in your friends list into your game and play together. However, your characters will not be different, because Steam Remote Play is basically a streaming function.
It will use the host's save game to create the second character, so the guest will have all of the hosts equipment, but not the same equipment that he has in his own game save file.

Have fun!!!