As a young man, Austin left Ireland for France where, at the age of 18, he entered the Society of Jesus in Nancy on 27 November 1735.
Betagh went on to become a Jesuit and in 1781 set up a number of free schools for the poor boys of Dublin.
Topham Bowden, an English writer, noted in his book, Tour through Ireland (1791), that "... Austin was a very remarkable character, of extraordinary learning and piety; he was a great preacher, and injured his health by his exertions in the pulpit."
The inscription over his grave describes him as "pius, doctus, indefessus operarius, apostolicis confectus laboribus.
Divites admonuit, pauperes sublevavit, juventutem erudivit, orphanis loco parentis fuit, de omni hominum genere prseclare meruit, omnibus omnia factus ut omnes Christo lucrifaceret."