In this study, we address a public R&D project portfolio selection problem with project cancellations. For several reasons, a funded R&D project may be halted before finishing the planned research. When a project is canceled, most of its budget is usually unused and also some of the spendings can return to the funding organization. In the call-based R&D programs, usually project selection decisions are made in one go, and, in the current call, it is not possible to award new projects with the unused budget. Decision-makers (DMs) of funding organizations can benefit from considering possible project cancellation situations to improve the budget utilization. We consider two cases. In the first case, we assume that cancellation probability of a project cannot be assessed but the DM can estimate the number of projects that will be canceled. In the second case, we assume that for each project, a cancellation probability can be assessed. For the first problem, we develop a mixed-integer linear programming formulation and a dynamic programming algorithm. For the second problem, we develop a chance-constrained stochastic programming formulation that can be solved as a mixed-integer second-order cone program. Our computational results show that practical-size problems can be solved by the proposed solution approaches.