What is the Order of Special Full-Time Servants? The Order of Special Full-Time Servants appears to be a religious order of Jehovah's Witnesses. What is a religious order in the context of Witness theology? Is it theologically  meaningful at all? To what purpose do people join this order? When do they leave? (Do they leave?) How does the whole thing work?
The different types of full time servants among Jehovah's Witnesses are:

Regular pioneers usually spend 70 hours a month in the field ministry. Some serve in a congregation where the need is greater.

Special pioneers usually spend 130 hours a month in the field ministry. They are often assigned to a congregation where the need is greater.

Circuit overseers visit congregations to help them improve in their ministry and encourage them in other ways.

Bethel family members serve in a branch office or a translation office. They help provide literature and direction for the ministry in the territory that is supervised by the branch.

Missionaries are usually assigned to serve in another country. Many missionaries spend 130 hours a month in the field ministry

International servants and volunteers go to various countries to assist with the construction of branch offices, remote translation offices, Assembly Halls, and Kingdom Halls.

Kingdom Hall construction servants are trained to build Kingdom Halls and assist with other construction projects in their own country.

For additional information  see the following article from the September 2014 Watchtower:
https://www.jw.org/en/publications/magazines/ws201409/remember-those-in-full-time-service/#link0

As for the specific title of your question there is indeed a group  called the Worldwide  Order of Special Full Time Servants. According to the April 2017 Watchtower:


  Currently, there are some 67,000 members of the Worldwide Order of Special Full-Time Servants of Jehovah’s Witnesses. Some perform Bethel service, others engage in construction or in circuit work, serve as field instructors or special pioneers or missionaries or as Assembly Hall or Bible school facility servants. They are all bound by a “Vow of Obedience and Poverty,” with which they agree to do whatever is assigned to them in the advancement of Kingdom interests, to live a simple lifestyle, and to abstain from secular employment without permission. It is not the people but their assignments that are viewed as special. They realize the seriousness of humbly living up to their solemn vow for as long as they remain in special full-time service. 


https://wol.jw.org/en/wol/d/r1/lp-e/2017365?q=special+order+of+full-time&amp;p=par