The State Council (cabinet) and Central Military Commission announced the penalties in a recent order, Xinhau news agency said.
It said Yu Deshui and Chen Qingyao, the commander and the political commissar of the force in Fujian province, were "deposed and given records of serious demerits."
Zhou Xiaomeng and Shi Gongsheng, the president and political commissar of the Fuzhou Armed Police Command School, were sacked from their posts both in the communist party and the armed police.
Hou Yongjun, director of the cadets' brigade, is to be prosecuted, the agency said.
Typhoon Longwang triggered sudden downpours and a landslide which destroyed the cadets' barracks.