Drive Dust Outside With a Fan
Cut the Jamb and Pull
You can knock a jamb sideways out of its opening, but the nails or screws holding it in place put up strong resistance to the shear force you apply.
An easier way is to cut one of the sides in half with a reciprocating saw and then pull the rest straight away from the framing. You can easily pull away any nails or screws holding the doorjambs in place simply by using the leverage of the jamb itself. Make your cut at an angle so the two cut sections don't wedge against each other, preventing you from pulling them apart. This same technique works for pulling out windows.