Rapid assembly and disassembly (turnover) of actin filaments in cytoplasm drives cell motility and shape remodeling. While many biochemical processes that facilitate filament turnover are understood in isolation, it remains unclear how they work together to promote filament turnover in cells. Here, we studied cellular mechanisms of actin filament turnover by combining quantitative microscopy with mathematical modeling. Using live cell imaging, we found that actin polymer mass decay in Listeria comet tails is very well fit by a simple exponential. By analyzing candidate filament turnover pathways using stochastic modeling, we found that exponential polymer mass decay is consistent with either slow treadmilling, slow Arp2/3-dissociation, or catastrophic bursts of disassembly, but is inconsistent with acceleration of filament turnover by severing. Imaging of single filaments in Xenopus egg extract provided evidence that disassembly by bursting dominates isolated filament turnover in a cytoplasmic context. Taken together, our results point to a pathway where filaments grow transiently from barbed ends, rapidly terminate growth to enter a long-lived stable state, and then undergo a catastrophic burst of disassembly. By keeping filament lengths largely constant over time, such catastrophic filament turnover may enable cellular actin assemblies to maintain their mechanical integrity as they are turning over.