In Fahrenheit 451, Beatty says "[Fire] is a mystery...Its real beauty is that it destroys responsibility and consquences." How has this been true?

Beatty says this when he and Montag are at Montag's house,
preparing to burn it down.  In the earlier parts of the book, we can see how fire (or at
least the way fire has been used in this society) has destroyed responsibility and
consequences.

In this society, fire has been used to burn
books.  This is part of a larger drive to rob people of their human impulses.  People
have been encouraged to ignore the real problems that come with being human.  They have
been encouraged to simply rid themselves of these problems by pretending they don't
exist.  True human life consists of having feelings and problems and confronting those
things and their consequences.  In this society, by contrast, people run from those
things.  We can see this clearly in how Mildred retreats into her parlor walls and in
how her friends try to forget their families.

When Beatty
says the line you cite, he is speaking figuratively.  His society's default reaction to
every problem is to burn it (literally or figuratively).  He is saying that they rid
themselves of responsibility and consequences by simply destroying their need to make
choices and confront problems.  This society does this by trying to get people to simply
live in the moment and forget that they are human beings.