Motivation: Seed filtering is critical in DNA read mapping, a process where billions of DNA fragments (reads) sampled from a donor are mapped onto a reference genome to identify genomic variants of the donor. Read mappers 1) quickly generate possible mapping locations (i.e., seeds) for each read, 2) extract reference sequences at each of the mapping locations, and then 3) check similarity between each read and its associated reference sequences with a computationally expensive dynamic programming algorithm (alignment) to determine the origin of the read. Location filters come into play before alignment, discarding seed locations that alignment would have deemed a poor match. The ideal location filter would discard all poor matching locations prior to alignment such that there is no wasted computation on poor alignments. Results: We propose a novel filtering algorithm, GRIM-Filter, optimized to exploit emerging 3D-stacked memory systems that integrate computation within a stacked logic layer, enabling processing-in-memory (PIM). GRIM-Filter quickly filters locations by 1) introducing a new representation of coarse-grained segments of the reference genome and 2) using massively-parallel in-memory operations to identify read presence within each coarse-grained segment. Our evaluations show that for 5% error acceptance rates, GRIM-Filter eliminates 5.59x-6.41x more false negatives and exhibits end-to-end speedups of 1.81x-3.65x compared to mappers employing the best previous filtering algorithm.