This is a separate issue to your issue of saving samples.
These are settings that describe how each of the Machinedrum’s drum tracks interacts with the other tracks.
The mute relation is used for interleaving drums, such as open and closed hi-hats which are supposed to stop the sound of each other when played.
The trigger relation is used for layering sounds.
You can read the full details on page 19 of the manual.