Understanding animal movement is a key challenge in ecology and conservation biology. Relocation data often represent a complex mixture of different movement behaviors, and reliably decomposing this mix into its component parts is an unresolved problem in movement ecology. Traditional approaches, such as composite random walk models, require that the timescales characterizing the movement are all similar to the usually arbitrary data-sampling rate. Movement behaviors such as long-distance searching and fine-scale foraging, however, are often intermixed but operate on vastly different spatial and temporal scales. An approach that integrates the full sweep of movement behaviors across scales is currently lacking. Here we show how the semivariance function (SVF) of a stochastic movement process can both identify multiple movement modes and solve the sampling rate problem. We express a broad range of continuous-space, continuous-time stochastic movement models in terms of their SVFs, connect them to relocation data via variogram regression, and compare them using standard model selection techniques. We illustrate our approach using Mongolian gazelle relocation data and show that gazelle movement is characterized by ballistic foraging movements on a 6-h timescale, fast diffusive searching with a 10-week timescale, and asymptotic diffusion over longer timescales.