In this work, we propose a semi-autonomous scheme to synergistically share the complicated task of manipulation and cutting of an unknown deformable tissue (U-DT) between a remote surgeon and a surgical robot. Particularly, utilizing the da Vinci Research Kit (dVRK) platform, we have designed and successfully demonstrated a fully functional shared control scheme for an autonomous tensioning and tele-cutting of a U-DT. We have shown the system’s ability to cooperate with a remote surgeon by leveraging an online data-driven learning and adaptive control method coupled with a reduced-order trajectory planning module that depends on just two parameters. By performing 25 experiments on custom-designed silicon phantoms and defining a set of success/failure metrics, we have put forward findings that establish a causal relationship between these two important parameters and the success or failure of the performed experiments.