Can SAM stop a dependency service/application if a SQL instance/DB stops or alerts?

You would want to make a custom alert and make sure that the trigger conditions are very exact so that it doesn't try and stop the service on the other host because of a false positive.

In that custom alert, you could add an alert action > Execute an external program. You'd have to call a custom script to stop the associated service on that server.

Obviously, this is very high level without knowing the specifics of the other node you want to stop services on.