Goe was educated at the King Edward's Grammar School, Louth and later at Hertford College, Oxford where he graduated B.A.
Goe had shown ability as a parish worker, preacher and organiser and in 1886 he was appointed the Bishop of Melbourne in succession to James Moorhouse.
Goe was aware of many problems in his church which needed attention but resolved that until the cathedral could be finished and paid for these must stand aside.
By that time the land boom had burst and for the next ten years Melbourne suffered from a severe depression.
Goe's wife died on 24 July 1901 and he resigned on 1 November 1901 but acted as administrator until his departure for England on 7 April 1902.