Demining is a subset of mine warfare. The term usually refers to clearing land mines after the end of conflict; it is sometimes called humanitarian demining. It is different from countermining, which is the removal, usually by combat engineers, of mines and improvised explosive devices that are encountered by regular military units.
Military units have far larger budgets for specialized equipment and trained personnel. They also may be concerned with only a small-scale problem of clearing a lane through a minefield, rather than rendering an area safe.
On the international level, organizations include the Geneva International Centre for Humanitarian Demining. 
"In May 1996, the United States Army Engineer School (USAES) at Fort Leonard Wood, Mo., established the Countermine Training Support Center (CTSC). In September of that year, the Office of the Assistant Secretary of Defense for Special Operations and Low Intensity Conflict (SO/LIC) established the Humanitarian Demining Training Center (HDTC) at Fort Leonard Wood. Both were created in direct response to the Presidential Landmine Policy Directive of May 1996. This document directs “[the] Department of Defense to …significantly expand itshumanitarian demining program to train and assist other countries in developing effective demining programs.” It further explains that the “government program is to train the trainers, including equipping the host nations to sustain their own demining programs. The State [DoS] and Defense Departments coordinate the funding and priorities to meet the demining needs of each individual nation.”