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We extend an agent-based multiscale model of vascular tumour growth and angiogenesis to describe transarterial chemoembolisation (TACE) therapies. The model accounts for tumour and normal cells that are both nested in a vascular system that changes its structure according to tumour-related growth factors. Oxygen promotes nutrients to the tissue and determines cell proliferation or death rates. Within the extended model TACE is included as a two-step process: First, the purely mechanical influence of the embolisation therapy is modelled by a local occlusion of the tumour vasculature. There we distinguish between partial and complete responders, where parts of the vascular system are occluded for the first and the whole tumour vasculature is destroyed for the latter. In the second part of the model, drug eluding beads (DEBs) carrying the chemotherapeutic drug doxorubicin are located at destroyed vascular locations, releasing the drug over a certain time-window. Simulation results are parameterised to qualitatively reproduce clinical observations. Patients that undergo a TACE-treatment are categorised in partial and complete responders one day after the treatment. Another 90 days later reoccurance or complete response are detected by volume perfusion computer tomography (VPCT). Our simulations reveal that directly after a TACE- treatment an unstable tumour state can be observed, where regrowth and total tumour death have the same likeliness. It is argued that this short time-window is favorable for another therapeutical intervention with a less radical therapy. This procedure can shift the outcome to more effectiveness. Simulation results with an oxygen therapy within the unstable time-window demonstrate a potentially positive manipulated outcome. Finally, we conclude that our TACE model can motivate new therapeutical strategies and help clinicians analyse the intertwined relations and cross-links in tumours.