The present disclosure is generally directed to vibratory separators that are used for processing drilling fluid, and in particular, vibratory separators that utilize electro-magnetic clamping apparatuses for attaching screen assemblies to a basket assembly. In one exemplary embodiment, an illustrative vibratory separator is disclosed which includes, among other things, a basket assembly having at least one screen support, and at least one screen assembly that is adapted to be releasably secured to the at least one screen support. Additionally, the disclosed vibratory separator also includes an electro-magnetic clamp apparatus that is adapted to releasably secure the at least one screen assembly to the at least one screen support when the electro-magnetic clamp apparatus is energized to a magnetized state, and to release the at least one screen assembly from the at least one screen support when the electro-magnetic clamp apparatus is de-energized to an un-magnetized state.