The problem of space debris removal from the near-Earth space is being studied in almost every country taking part in space exploration. This is due to the global threat of critical increase in the number of space debris objects predicted for the near future, in particular as a result of significant growth in demand for multi-satellite constellations for various purposes. To date, researchers have proposed a large number of different methods for space debris removal. The work presented is the development of one of the promising contactless methods of space debris removal by an ion beam. The results of modeling and optimization of physical processes in the ion source to be mounted on board a service spacecraft that is necessary for implementing the considered method of space debris removal are presented. Besides, the results of thermal modeling and thermal mapping of the ion source during its operation are presented also, and the calculation results of its output parameters are compared to experimental data, which verified the small divergence angles of the generated ion beam. To assess the prospects of using a system for contactless space debris transportation by an ion beam using the obtained data on the operating parameters of the ion source, the trajectory design and mission analysis were carried out, which revealed the feasibility of removing seven space debris objects out of the protected region in geostationary orbit by a single service spacecraft. Besides, the preliminary service spacecraft design is presented.