What is known for certain, per Juno's warning to the Maitlands, is that Betelgeuse was once Juno's assistant (which implies he committed suicide in life since working for her counts as being a civil servant. The explanation of his suicide by hanging was left out of the film) but he was a troublemaker.

Does Beetlejuice kill himself?

Beetlejuice died by suicide. He is Juno's assistant and thus a civil servant. The film explains that civil servants all took their own lives.

How did Beetlejuice end?

Beetlejuice has a pretty upbeat ending, considering the protagonists are dead. Lydia has just scored an A on the math test and the Maitlands and Deetzes are living happily together in their newly restored New England cottage.