Originally working in brickmaking in Belfast, he invented machines used in that trade, before patenting the screw-pile in 1833, for which he would later gain some fame.

[3][4] The screw-pile was used for the erection of lighthouses and other structures on mudbanks and shifting sands, including bridges and piers.

In May 1851 he moved to Cobh to lay the foundation for a lighthouse on the Spit Bank;[5] the success of these undertakings led to the use of his invention on the breakwater at Portland, the viaduct and bridges on the Bombay, Baroda and Central India Railway and a broad system of Indian telegraphs.

While in Cork, Mitchell became friendly with astronomer John Thomas Romney Robinson, and mathematician George Boole.

In 1848, he was elected a member of the Institution of Civil Engineers and received the Telford Medal the same year for a paper on his invention.