Mobile Warfare is the correct English phrase for Mao Zedong's main military methods. For the general topic of military mobility, see maneuver warfare.
The achievements of Mao and the Communists in the Chinese Civil War are normally referred to as Guerrilla warfare. But he himself made a distinction between Mobile Warfare ( yundong zhan), Positional Warfare ( zhendi zhan) and Guerrilla warfare ( youji zhan).
Mao had a regular army that was far too big to hide, but made a point of conceding territory and avoiding battle until he was ready to fight.
The most notable example was the Long March, a massive military retreat in which Mao marched in circles in Guizhou until he had confused the vastly larger armies pursuing him, and was then able to slip through Yunnan and Sichuan, although the retreat was completed by only one-tenth of the force that left for the Long March at Jiangxi. A sensible comparison would be Robert E. Lee's surrender at Appomattox Court House, though he was never outnumbered to the degree Mao regularly was.
These military methods were part of the military-political strategy of People's war, which aims to win the support of the local population.
The Chinese People's Volunteer Army's first five campaigns in the Korean War were Mobile Warfare, in which the PVA encircled the enemy through maneuvers and sought to annihilate the enemy. Then it entered a stage of Positional Warfare, when both the PVA and UN forces fought to a stalemate along the 38th parallel north.
Seeking Truth From Facts: RAND 1991, page 136. The book is mostly about post-Mao developments within the Chinese military.
- See also here http://www.au.af.mil/au/aul/bibs/great/mao.htm for various English-language sources using the phrase.