This paper presents a theory of harvesting for biological assets with size-dependent stochastic growth that allows for partial harvests and accounts for the risk of extinction. The harvesting decision is formulated as a disinvestment problem in continuous time using real options and general harvesting rules are derived. The probability of extinction is then analyzed for a wide class of growth functions. A dimensionless analysis of a logistic Brownian motion shows that the optimal biomass at harvest and the amount harvested do not vary monotonically with uncertainty. More generally, this paper demonstrates the importance of boundary conditions in stochastic investment problems.