The world’s biggest container-ship operator is altering course, slashing jobs and canceling or delaying orders for new vessels after years weathering a sharp downturn in the container-shipping market.

Danish conglomerate A.P. Møller-Maersk A/S said Wednesday its Maersk Line container-shipping unit would cut 4,000 jobs from its land-based staff of 23,000. It is also canceling options to buy six Triple-E vessels, the world’s largest container ships, to cope with the deepest market slump in the industry since the 2009 global...