Benchmarks like GSM8K are popular measures of mathematical reasoning, but leaderboard gains can overstate true capability due to memorization of fixed test sets. Most robustness variants apply surface-level perturbations (paraphrases, renamings, number swaps, distractors) that largely preserve the underlying facts, and static releases can themselves become memorization targets over time. We introduce GSM-SEM, a reusable and stochastic framework for generating semantically diverse benchmark variants with substantially higher semantic variance than prior approaches. GSM-SEM perturbs problem statements by modifying entities, attributes, and/or relationships, frequently altering underlying facts and requiring models to recompute solutions under new conditions, while constraining generation to preserve the original calculations/answer and approximate problem difficulty. GSM-SEM generates fresh variants on each run without requiring re-annotation, reducing reliance on static public benchmarks for evaluation and thereby lowering the bias of memorization. We apply GSM-SEM on GSM8K and two existing variation suites (GSM-Symbolic and GSM-Plus), producing GSM8K-SEM, GSM-Symbolic-SEM, and GSM-Plus-SEM. Evaluating 14 SOTA LLMs, we observe consistent performance drops with larger decline when semantic perturbations are coupled with symbolic/plus variations (average drop rate 28% in maximum strictness configuration of GSM-SEM). We publicly release the three SEM variants as fully human-validated datasets. Finally, to demonstrate applicability beyond GSM-style math problems, we apply GSM-SEM to additional benchmarks including BigBenchHard, LogicBench, and NLR-BIRD.