The occupation "Wagner" translates to carriage maker (cartwright).
It is very unlikely that the name could have been spelled Refsel because that would be difficult to pronounce. In contrast, nothing is wrong with the spelling Ressel. The reading of Refsel might come from having the name written in old German longhand ("Kurrent"). In the Kurrent script, the two letters s in Ressel are written differently. The first of the two s'es is written somewhat similarly to the letters f, t, or h.
The name Ressel is well known in Austria because of the inventor Josef Ressel, whom the Austrians (and Czechs) consider to be the inventor of the underwater ship propeller. Josef Ressel was born in Chrudim/Bohemia. The wikipedia article on Ressel mentions a book with a genealogy of Josef Ressel.
The picture of Ressel is known well to most living Austrians because it was on the 500 Schilling banknote before Austria became a founding member of the Euro zone.