The growth of space debris in Earth's orbit is recognized as a serious threat to future space missions. To contain the growth of space debris in the long term, active removal of large defunct spacecraft is needed. A promising solution to this problem is the use of tether-nets. In the envisaged mission, a net is released from a chaser spacecraft toward a target debris; the net entangles the debris and the tether provides a flexible link between chaser and debris to tug the debris to a disposal orbit. The present work is focused on the simulation and control of a tether-actuated closing mechanism. In this concept, proposed only recently, the tether is looped through the center of the net and around the perimeter, and spooling the tether in draws the net perimeter closed. In this paper, a dynamic model of a tether-actuated closing mechanism for net-based capture of space debris is developed. The model of the winch, which is key to the control of the closing mechanism, is established based on literature on the design of reeling mechanisms for tether-nets. Two control laws for the winch velocity during deployment and closure of the net, respectively, are formulated and tested in simulation. Simulations of the capture of a Zenit-2 rocket upper stage are performed using a proportional-derivative tension control law with gain scheduling based on tether length. Results support feasibility of the tether-actuated closing mechanism.