Aspiration thrombectomy is a treatment option for ischemic stroke due to occlusions in large vessels. During the therapy a device is inserted into the vessel and suction is applied. A new one-dimensional model is introduced that is capable of simulating this procedure while accounting for the fluid-structure interactions in blood flow. To solve the coupling problem at the tip of the device a problem-suited Riemann solver is constructed based on relaxation of the hyperbolic model. Numerical experiments investigating the role of the catheter size and the suction forces are presented