Orbital angular momentum (OAM) mode multiplexing provides a new strategy for reconstructing multiple holograms, which is compatible with other physical dimensions involving wavelength and polarization to enlarge information capacity. Conventional OAM multiplexing holography usually relies on the independence of physical dimensions, and the deep holography involving spatial depth is always limited for the lack of spatiotemporal evolution modulation technologies. Herein, we introduce a depth-controllable imaging technology in OAM deep multiplexing holography via designing a prototype of five-layer optical diffractive neural network (ODNN). Since the optical propagation with dimensional-independent spatiotemporal evolution offers a unique linear modulation to light, it is possible to combine OAM modes with spatial depths to realize OAM deep multiplexing holography. Exploiting the multi-plane light conversion and in-situ optical propagation principles, we simultaneously modulate both the OAM mode and spatial depth of incident light via unitary transformation and linear modulations, where OAM modes are encoded independently for conversions among holograms. Results show that the ODNN realized light field conversion and evolution of five multiplexed OAM modes in deep multiplexing holography, where the mean square error and structural similarity index measure are 0.03 and 86%, respectively. Our demonstration explores a depth-controllable spatiotemporal evolution technology in OAM deep multiplexing holography, which is expected to promote the development of OAM mode-based optical holography and storage.