  The Merriman-Bence-Osher threshold dynamics method is an efficient algorithm
to simulate the motion by mean curvature. It has the advantages of being easy
to implement and with high efficiency. In this paper, we propose a threshold
dynamics method for dislocation dynamics in a slip plane, in which the spatial
operator is essentially an anisotropic fractional Laplacian. We show that this
threshold dislocation dynamics method is able to give { two correct leading
orders} in dislocation velocity, including both the $O(\log\varepsilon)$ local
curvature force and the $O(1)$ nonlocal force due to the long-range stress
field generated by the dislocations as well as the force due to the applied
stress, where $\varepsilon$ is the dislocation core size, { if the time step is
set to be $\Delta t=\varepsilon$. This generalizes the available result of
threshold dynamics with the corresponding fractional Laplacian, which is on the
leading order $O(\log\Delta t)$ local curvature velocity under the isotropic
kernel.} We also propose a numerical method based on spatial variable
stretching to correct the mobility and to rescale the velocity for efficient
and accurate simulations, which can be applied generally to any threshold
dynamics method. We validate the proposed threshold dislocation dynamics method
by numerical simulations of various motions and interaction of dislocations.
