It follows reports that President Trump was outraged by comments made by Mulvaney during the Ukraine corruption saga.
The allegations of abuse of power over the Ukraine incident led to impeachment proceedings against President Trump.
Mulvaney's departure has been on the cards for the last few weeks.
Mr Mulvaney is to become US special envoy to Northern Ireland, while North Carolina lawmaker Mark Meadows has been appointed to take over his former position.
Trump says US, Iran agree to continue talks but ceasefire over
President Donald Trump said the US and Iran had agreed to continue talks despite an escalation of hostilities this week but he declared that the ceasefire reached between the two sides last month was over.
Russian strikes kill seven, wound dozens, Ukraine's Zelenskiy seeks faster weapons deliveries
Russia launched missile and drone attacks on Ukraine on Saturday, killing seven people and wounding dozens more, officials said, as President Volodymyr Zelenskiy called for diplomatic efforts to ensure Kyiv secured weapons more quickly.
Venezuela quakes have killed 4,333, injured 16,740, National Assembly president says
The death toll from the two earthquakes that struck Venezuela on June 24 has risen to 4,333, National Assembly President Jorge Rodriguez told reporters on Saturday, announcing that the distribution of housing to those affected will begin next week.
Floods in Bangladesh kill 44, leave over a million stranded
Floods and landslides triggered by days of torrential monsoon rain have killed at least 44 people in southeastern Bangladesh and left over a million stranded as authorities raced on Saturday to deliver aid to devastated communities.
Typhoon Bavi makes landfall in eastern China's Taizhou after nearly 2 million evacuated
Typhoon Bavi made landfall late on Saturday in the coastal city of Taizhou in eastern China, where nearly 2 million people were evacuated, having earlier pummelled Japan's southern Sakishima island chain and brushed past northern Taiwan.
