How do Elixir with Mix make a daemon?

You can use the --detached option to start the runtime system detached from the system console. It is meant to be used for running daemons and backgrounds processes:

elixir --detached -S mix run

Regarding reltool, you can use exrm although and pass -detached (single -) when configuring the VM arguments. The full argument list for the runtime system can be found here: http://erlang.org/doc/man/erl.html