This paper presents the mission concept and engineering design of a debris-removing nanosatellite called Deorbiter CubeSat, within the framework of NASA’s Pre-Phase A studies. The spacecraft is designed based on the utilization of an eight-unit form factor, and is intended for the removal of predetermined sizable debris objects from the low Earth orbit. A number of attitude and orbit determination sensors and control actuators are included on the CubeSat, which are employed during the rendezvous, attachment, and deorbiting operations. Upon attaching to a debris, the CubeSat stabilizes the rotational motion of the debris, and then proceeds to reducing the debris orbit size, in order to re-enter Earth’s atmosphere and burn up due to the high atmospheric density. The engineering design of Deorbiter CubeSat is outlined, and the selected components are detailed. The selected components are commercially available and have long space heritage. System’s mass budget is analyzed, and preliminary component costs are estimated. Three scenarios for the Deorbiter CubeSat mission operations are considered, and the spacecraft power budget and components duty cycles are investigated for each scenario. In light of the results, the feasibility of each scenario for the Deorbiter CubeSat mission is discussed.