Computer-aided design (CAD) plays an essential role in creative idea generation on 2D screens during the design process. In most CAD scenarios, virtual object translation is an essential operation, and it is commonly used when designers simulate their innovative solutions. The degrees of freedom (DoF) of virtual object translation modes have been found to directly impact users’ task performance and psychological aspects in simulated environments. Little is known in the existing literature about the sense of agency (SoA), which is a critical psychological aspect emphasizing the feeling of control, in translation modes on 2D screens during the design process. Hence, this study aims to assess users’ SoA in virtual object translation modes on mouse-based, touch-based, and handheld augmented reality (AR) interfaces through subjective and objective measures, such as self-report, task performance, and electroencephalogram (EEG) data. Based on our findings in this study, users perceived a greater feeling of control in 1DoF translation mode, which may help them come up with more creative ideas, than in 3DoF translation mode in the design process; additionally, the handheld AR interface offers less control feel, which may have a negative impact on design quality and creativity, as compared with mouse- and touch-based interfaces. This research contributes to the current literature by analyzing the association between virtual object translation modes and SoA, as well as the relationship between different 2D interfaces and SoA in CAD. As a result of these findings, we propose several design considerations for virtual object translation on 2D screens, which may enable designers to perceive a desirable feeling of control during the design process.