Could not compile dependency :mint

To summarize the problem/solution, in this thread, for future reference:

Elixir and Erlang are both languages that run on the BEAM VM, but the BEAM is (primarily) installed on systems by installing Erlang/OTP. The Elixir compiler itself is (currently) written in Erlang. So, you will generally need to install Erlang before you can install a working Elixir.

In this instance, the -otp-27 part of mise install elixir@1.18.3-otp-27 indicates that you want a version of Elixir that can compile with an instance of Erlang/OTP that is version 27, hence the need to mise install erlang@27.x first.