Brain-computer interface (BCI) based on steady-state visual evoked potential (SSVEP) have attracted much attention in the field of intelligent robotics. Traditional SSVEP-based BCI systems mostly use synchronized triggers without identifying whether the user is in the control or non-control state, resulting in a system that lacks autonomous control capability. Therefore, this paper proposed a SSVEP asynchronous state recognition method, which constructs an asynchronous state recognition model by fusing multiple time-frequency domain features of electroencephalographic (EEG) signals and combining with a linear discriminant analysis (LDA) to improve the accuracy of SSVEP asynchronous state recognition. Furthermore, addressing the control needs of disabled individuals in multitasking scenarios, a brain-machine fusion system based on SSVEP-BCI asynchronous cooperative control was developed. This system enabled the collaborative control of wearable manipulator and robotic arm, where the robotic arm acts as a “third hand”, offering significant advantages in complex environments. The experimental results showed that using the SSVEP asynchronous control algorithm and brain-computer fusion system proposed in this paper could assist users to complete multitasking cooperative operations. The average accuracy of user intent recognition in online control experiments was 93.0%, which provides a theoretical and practical basis for the practical application of the asynchronous SSVEP-BCI system.