This paper studies an underlay-based cognitive two-way relay network which consists of a primary network (PN) and a secondary network (SN). Two secondary users (SUs) exchange information with the aid of multiple single-antenna amplify-and-forward relays while a primary transmitter communicates with a primary receiver in the same spectrum. Unlike the existing contributions, the transmit powers of the SUs and the distributed beamforming weights of the relays are jointly optimized to minimize the sum interference power from the SN to the PN under the quality-of-service (QoS) constraints of the SUs determined by their output signal-to-interference-plus-noise ratio (SINR) and the transmit power constraints of the SUs and relays. This approach leads to a non-convex optimization problem which is computationally intractable in general. We first investigate two necessary conditions that optimal solutions should satisfy. Then, the non-convex minimization problem is solved analytically based on the obtained conditions for single-relay scenarios. For multi-relay scenarios, an iterative numerical algorithm is proposed to find suboptimal solutions with low computational complexity. It is shown that starting with an arbitrarily initial feasible point, the limit point of the solution sequence derived from the iterative algorithm satisfies the two necessary conditions. To apply this algorithm, two approaches are developed to find an initial feasible point. Finally, simulation results show that on average, the proposed low-complexity solution considerably outperforms the scheme without source power control and performs close to the optimal solution obtained by a grid search technique which has prohibitively high computational complexity.