Secure computation of federated multi-party databases can perform federated querying or federated modeling on private data from multiple databases while preserving data privacy. Such a federation is typically a loosely organized group where the participating databases may dropout unexpectedly. However, existing multi-party secure computation systems usually employ privacy-preserving computation schemes like secret sharing, which require participants to remain online, resulting in poor system availability. Moreover, these systems are unable to predict the number of users or request rates when providing services externally. If the system is deployed on a private cluster or rented virtual machines from a cloud computing platform, it will experience increased latency during sudden bursts of requests and resource waste when the request workload is low, leading to poor overall scalability of the system. With the advancement of cloud computing technology, serverless computing has emerged as a new cloud-native deployment paradigm that offers excellent elastic resource scaling. This study designs a system architecture and an indirect communication scheme within the serverless computing framework to architect a highly scalable and highly available multi-party database secure computation system. This system can tolerate database node disconnections and automatically scale system resources in response to user request traffic changes. A system prototype based on Alibaba Cloud and OceanBase database is implemented. Comprehensive experimental comparisons are conducted. The results show that the proposed system outperforms existing systems in terms of computational cost, system performance, and scalability for tasks such as low-frequency queries and horizontal modeling. It can save up to 78% in computational costs and improve system performance by over 1.6 times. The shortcomings of the proposed system for tasks such as complex queries and vertical modeling are analyzed.