Integrated sensing and communications (ISAC) is a key enabler of new applications, such as precision agriculture, extended reality (XR), and digital twins, for 6G wireless systems. However, the implementation of ISAC technology is very challenging due to practical constraints such as high complexity. In this paper, we introduce a novel ISAC waveform design strategy, called the spatial-division ISAC (SD-ISAC) waveform, which simplifies the ISAC waveform design problem by decoupling it into separate communication and radar waveform design tasks. Specifically, the proposed strategy leverages the null-space of the communication channel to superimpose sensing signals onto communication signals without interference. This approach offers multiple benefits, including reduced complexity and the reuse of existing communication and radar waveforms. We then address the problem of optimizing the spatial and temporal properties of the proposed waveform. We develop a low-complexity beampattern matching algorithm, leveraging a majorization-minimization (MM) technique. Furthermore, we develop a range sidelobe suppression algorithm based on manifold optimization. We provide comprehensive discussions on the practical advantages and potential challenges of the proposed method, including null-space feedback. We evaluate the performance of the proposed waveform design algorithm through extensive simulations. Simulation results show that the proposed method can provide similar or even superior performance to existing ISAC algorithms while reducing computation time significantly.