Online psychological counseling dialogue systems come into the trend, offering a convenient and accessible alternative to traditional in-person therapy. However, existing psychological counseling dialogue systems mainly focus on single-type empathetic dialogue with minimal professional knowledge. In many real-life counseling scenarios, clients often seek multi-type help, such as diagnosis, consultation, therapy, console, and common questions, but struggle to identify clear and specific goals due to their limited experience and knowledge. In this paper, we identify this challenge as how to construct mixed-type dialogue systems for psychological counseling that enable clients to first clarify their goals before proceeding with counseling. To mitigate the challenges, we collect a mixed-type counseling dialogues corpus, covering five dialogue types: task-oriented dialogue for diagnosis, knowledge-grounded dialogue, recommendation, empathetic dialogue, and question answering. Moreover, spatiotemporal-aware knowledge enables systems world aware and has been proven to affect one's mental health. Therefore, we link dialogues to spatiotemporal state and propose a spatiotemporal-aware mixed-type psychological counseling dataset, termed STAMPsy, containing 5k mixed-type conversations and 62K utterances. Additionally, we build baselines on STAMPsy and develop a psychological dialogue generation framework with iterative self-feedback, named Self-STAMPsy. Results indicate that clarifying dialogue goals in advance and utilizing spatiotemporal states are effective. STAMPsy will be publicly available at github.com.