This paper studies a secrecy unmanned aerial vehicle (UAV) communication system with coordinated multi-point (CoMP) reception, in which one UAV sends confidential messages to a set of cooperative ground receivers (GRs), in the presence of several suspicious eavesdroppers. In particular, we consider two types of eavesdroppers that are non-colluding and colluding, respectively. Under this setup, we exploit the UAV's maneuver in three dimensional (3D) space together with transmit power adaptation for optimizing the secrecy communication performance. First, we consider the quasi-stationary UAV scenario, where we jointly optimize the UAV's 3D placement and transmit power control to maximize the secrecy rate. Under both non-colluding and colluding eavesdroppers, we obtain the optimal solutions to the joint 3D placement and transmit power control problems in well structures. Next, we consider the mobile UAV scenario, where we jointly optimize the UAV's 3D trajectory and transmit power allocation to maximize the average secrecy rate during the whole communication period. To deal with the difficult joint 3D trajectory and transmit power allocation problems, we present alternating-optimization-based approaches to obtain high-quality solutions. Finally, we provide numerical results to validate the performance of our proposed designs. It is shown that due to the consideration of CoMP reception, our proposed design with 3D maneuver significantly outperforms the conventional design with two dimensional (2D) (horizontal) maneuver only, by exploiting the additional degrees of freedom in altitudes. It is also shown that the non-colluding and colluding eavesdroppers lead to distinct 3D UAV maneuver behaviors.