Large-scale web-crawled datasets contain noise, bias, and irrelevant information, necessitating data selection techniques. Existing methods depend on hand-crafted heuristics, downstream datasets, or require expensive influence-based computations -- all of which limit scalability and introduce unwanted data dependencies. To address this, we introduce the Mimic Score, a simple and geometry-based data-quality metric that evaluates utility by measuring alignment between a sample's gradients and a target direction induced by a pre-trained reference model. This leverages readily available model weights, avoids needing validation datasets, and incurs minimal computational overheads. Building on this metric, we propose Grad-Mimic, a two-stage framework that re-weights samples online to accelerate training and aggregates sample utilities offline to construct effective data filters. Empirically, we show that using mimic scores to guide training improves data efficiency, accelerates convergence, yields consistent performance gains across six image datasets, and enhances CLIP models with 20.7% fewer training steps. Additionally, mimic score-based filters augment existing filtering techniques, enabling improved CLIP models trained with 4.7 million fewer samples.