The Inda series by Sherwood Smith.
From the author's glossary:
WASTE SPELL: The simple definition is that these few syllables, whispered when a human being lets go of waste, gets rid of it. Waste includes vomit, and with a syllable attached, menses. The Spell dates back to the earliest days after humans first found themselves on this world, and the indigenous beings, discovering that not only were humans fast befouling the environment they were making themselves sick, communicated the connection to the early mages, who, when they comprehended the connection, not only arranged for this magic (for the curious, the waste is broken down chemically and transported deep underground), they arranged for spells that could be performed over specific items, such as buckets, that not just cleaned the water of bacteria, but cleaned items dipped into the buckets.
WANDING: Wands have spells on them to break down and transfer animal waste underground.