As an attractive alternative to traditional and large satellite, small satellite cluster (SSC) with low cost and short development time will play an important role in Earth observation. Generally, SSC networks for Earth observation are energy-limited, the design of the joint data downloading and resource management scheme remains challenging. On the one hand, with the ever-increasing amount of sensing data, multiple gateway stations and relay satellites have been deployed to receive the sensing data from SSC. The problem that where to download the sensing data should be addressed. On the other hand, due to the limited communication, storage, computing and power supply capacities of small satellite, an efficient multi-dimensional resource management scheme should be adopted. In this paper, the joint data downloading scheduling and multi-dimensional resource management problem for satellite cluster networks with relay satellites is investigated, which is formulated as a long-term optimization problem to minimize the energy consumption and guarantee the data drop rate performance. Then, this problem is decomposed into a series of mixed-integer programming problems by Lyapunov optimization theory. Leveraging many-to-many matching theory with empty node and the simplex method, an online joint data downloading and resource management (OJDDRM) scheme is proposed. Simulation results validate the proposed OJDDRM scheme's performance and demonstrate that there exists a balance point for the proposed OJDDRM scheme. Under the balance point, the data drop rate is zero and the energy consumption can be reduced compared with the existed schemes.