A battery separator having a thermal shutdown mechanism and exhibiting excellent mechanical properties and low electrical resistance includes a water-scavenging and/or acid-scavenging material having reactive functional groups that chemically react with water or acid in the battery to remove the water or acid and thereby improve battery performance. The battery separator preferably includes a first polyolefin providing mechanical integrity and a second polyolefin including the water-scavenging or acid-scavenging reactive functional groups. The battery separator is preferably a microporous film including a polymer matrix throughout which the water-scavenging or acid-scavenging material is dispersed.