Mulock was a sub-lieutenant on the relief ship Morning, attached to Scott's National Antarctic Expedition, 1901 - 04, transferring to the shore party in March 1903 in exchange for Ernest H Shackleton on account of his skills as a cartographer and surveyor.
Mulock was just 21 when he transferred to Discovery, In September 1903 he accompanied Lt Michael Barne on what was to be a ten-week southern journey to explore an inlet of the Western Mountains; weather and surface conditions drove them back soon after they had reached Barne Glacier. The temperature fell to -67.7 Fahrenheit and Seaman Ernest E. Joyce got badly frost-bitten feet. The situation grew so serious that Barne and Mulock took turns to hold them against the pits of their stomachs and knead the ankles for several hours, saving his feet from certain amputation.

Scott had a very high opinion of Mulock's abilities and initiative, frequently recording praise of him in his diaries. In his written account of the expedition, Captain R F Scott wrote "Mulock was then only twenty-one years of age but having a natural bent for his work, his services proved invaluable". On the return of the expedition, King Edward VII awarded the Silver Polar Medal.