He was suggested to Gill by his father Herbert William Cribb's associate, the Arts and Crafts printer Emery Walker.
He completed his apprenticeship in 1913, but continued working with Gill, particularly on the Westminster Cathedral Stations of the Cross until his army service in France, 1916–19.
Joseph remained at the Guild and took over Gill's workshop, establishing his own practice as a sculptor, carver and letter cutter.
At the time of his death he was running a successful business, employing two assistants, Noel Tabbenor and Kenneth Eager.
Examples of his letter cutting and carving can be seen in Ditchling Museum and next door in St Margaret's Church and its churchyard, where his own grave is to be found, marked with a stone made in his workshop by his assistant Kenneth Eager.