Briefly explain why cutting a flatworm into pieces would not kill it

Cleaving a flatworm into pieces would not kill the flatworm as each piece would turn into a new flatworm. The mechanism is known as fragmentation. In multicellular species, fragmentation refers to a kind of asexual reproduction in which a species gets cleaved into fragments.  

Each of these fragments forms into completely developed, mature individuals, which are similar to their parents. Fragmentation is also called splitting, it is a mode of reproduction witnessed in various species like molds, filamentous cyanobacteria, lichens, various plants, and animals like flatworms, sponges, sea stars, and some annelids.