  Many theories of dark matter beyond the Weakly Interacting Massive Particles
(WIMP) paradigm feature an enhanced matter power spectrum on sub-parsec scales,
leading to the formation of dense dark matter minihaloes. Future local
observations are promising to search for and constrain such substructures. The
survival probability of these dense minihaloes in the Milky Way environment is
crucial for interpreting local observations. In this work, we investigate two
environmental effects: stellar disruption and (smooth) tidal disruption. These
two mechanisms are studied using semi-analytic models and idealized N-body
simulations. For stellar disruption, we perform a series of N-body simulations
of isolated minihalo-star encounters to test and calibrate analytic models of
stellar encounters before applying the model to the realistic Milky Way disk
environment. For tidal disruption, we perform N-body simulations to confirm the
effectiveness of the analytic treatment. Finally, we propose a framework to
combine the hierarchical assembly and infall of minihaloes to the Milky Way
with the late-time disruption mechanisms. We make predictions for the mass
functions of minihaloes in the Milky Way. The survival fraction of dense dark
matter minihaloes, e.g. for axion miniclusters and minihaloes from Early Matter
Domination, is $\sim 60\%$ with the relatively low-mass, compact population
surviving. The survival fraction is insensitive to the detailed model
parameters. We discuss various implications of the framework and future direct
detection prospects.
