Sure, this is entirely possible with the appropriate motors, mechanics, and safety features, but the machine would not be without quite a bit of design effort. This will, of course, depend on what type of cut off saw desired, design for the feeding mechanism, the jigs and supports necessary for the object being cut, and the size and material of the object being cut. There are way too many variables to specify on this limited questions and answer forum, but with some research, anything is possible.
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Would it be possible and without excessive effort, to build an automatic conveyor fed cuttoff saw?