“I think my silhouette, the shape of my body, is of comfort to my patients on some level,” BJ Miller says. In 1990, the palliative care doctor lost both legs below the knee and his left arm below the elbow when 11,000 volts of electricity shot through his body after he scaled a commuter train with some friends. Miller is now a celebrity of sorts, applauded for the innovative approach to palliative care he took at the Zen Hospice in San Francisco. This July, Miller will publish a book (co-written with Shoshana Berger) titled A Beginner’s Guide to the End. Talking to Ben Shattuck, he explains why we must rethink our approach to the inevitable.

The work you do is very personal—helping people face suffering and their own mortality. Has it been difficult to talk about that so publicl...