Sparse Tucker Decomposition (STD) algorithms learn a core tensor and a group of factor matrices to obtain an optimal low-rank representation feature for the High-Order, High-Dimension, and Sparse Tensor (HOHDST). However, existing STD algorithms face the problem of intermediate variables explosion which results from the fact that the formation of those variables, i.e., matrices Khatri-Rao product, Kronecker product, and matrix-matrix multiplication, follows the whole elements in sparse tensor. The above problems prevent deep fusion of efficient computation and big data platforms. To overcome the bottleneck, a novel stochastic optimization strategy (SGD__Tucker) is proposed for STD which can automatically divide the high-dimension intermediate variables into small batches of intermediate matrices. Specifically, SGD__Tucker only follows the randomly selected small samples rather than the whole elements, while maintaining the overall accuracy and convergence rate. In practice, SGD__Tucker features the two distinct advancements over the state of the art. First, SGD__Tucker can prune the communication overhead for the core tensor in distributed settings. Second, the low data-dependence of SGD__Tucker enables fine-grained parallelization, which makes SGD__Tucker obtaining lower computational overheads with the same accuracy. Experimental results show that SGD__Tucker runs at least 2XX faster than the state of the art.