Photonic computing has emerged as a promising solution for accelerating computation-intensive artificial intelligence (AI) workloads. However, limited reconfigurability, high electrical-optical conversion cost, and thermal sensitivity limit the deployment of current optical analog computing engines to support power-restricted, performance-sensitive AI workloads at scale. Sparsity provides a great opportunity for hardware-efficient AI accelerators. However, current dense photonic accelerators fail to fully exploit the power-saving potential of algorithmic sparsity. It requires sparsity-aware hardware specialization with a fundamental re-design of photonic tensor core topology and cross-layer device-circuit-architecture-algorithm co-optimization aware of hardware non-ideality and power bottleneck. To trim down the redundant power consumption while maximizing robustness to thermal variations, we propose SCATTER, a novel algorithm-circuit co-sparse photonic accelerator featuring dynamically reconfigurable signal path via thermal-tolerant, power-efficient in-situ light redistribution and power gating. A power-optimized, crosstalk-aware dynamic sparse training framework is introduced to explore row-column structured sparsity and ensure marginal accuracy loss and maximum power efficiency. The extensive evaluation shows that our cross-stacked optimized accelerator SCATTER achieves a 511X area reduction and 12.4X power saving with superior crosstalk tolerance that enables unprecedented circuit layout compactness and on-chip power efficiency.