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A major issue for needle insertion into soft tissue during suturing is the induced tissue deformation that hinders the minimization of tip-target positioning error. In this letter, we present a new robot control framework to solve target deviation by integrating active deformation control. We characterize the motion behavior of the desired target under needle-tissue interaction by introducing the needle-induced deformation matrix. Note that the modeling does not require the exact knowledge of tissue or needle insertion properties. The unknown parameters are online updated during the insertion procedure by an adaptive estimator via sensor-based measurement. A closed-loop controller is then proposed for dualarm robotic execution upon image guidance. The dual-arm control aims to regulate a feature vector concerning the tip-target alignment to ensure target reachability. The feasibility of the proposed algorithm is studied via simulations and experiments on different biological tissues to simulate robotic minimally-invasive suturing using the da Vinci Research Kit as the control platform.