Joint time-vertex graph signals are pervasive in real-world. This paper focuses on the fundamental problem of sampling and reconstruction of joint time-vertex graph signals. We prove the existence and the necessary condition of a critical sampling set using minimum number of samples in time and graph domain respectively. The theory proposed in this paper suggests to assign heterogeneous sampling pattern for each node in a network under the constraint of minimum resources. An efficient algorithm is also provided to construct a critical sampling set.