Given an untrimmed video and a sentence query, video moment retrieval using language (VMR) aims to locate a target query-relevant moment. Since the untrimmed video is overlong, almost all existing VMR methods first sparsely down-sample each untrimmed video into multiple fixed-length video clips and then conduct multi-modal interactions with the query feature and expensive clip features for reasoning, which is infeasible for long real-world videos that span hours. Since the video is downsampled into fixed-length clips, some query-related frames may be filtered out, which will blur the specific boundary of the target moment, take the adjacent irrelevant frames as new boundaries, easily leading to cross-modal misalignment and introducing both boundary-bias and reasoning-bias. To this end, in this paper, we propose an efficient approach, SpotVMR, to trim the query-relevant clip. Besides, our proposed SpotVMR can serve as plug-and-play module, which achieves efficiency for state-of-the-art VMR methods while maintaining good retrieval performance. Especially, we first design a novel clip search model that learns to identify promising video regions to search conditioned on the language query. Then, we introduce a set of low-cost semantic indexing features to capture the context of objects and interactions that suggest where to search the query-relevant moment. Also, the distillation loss is utilized to address the optimization issues arising from end-to-end joint training of the clip selector and VMR model. Extensive experiments on three challenging datasets demonstrate its effectiveness.