If your free travel on the clutch pedal is within specs, and assuming that the clutch plate is not stuck to the flywheel as mentioned above, then I would have to assume that it is either some worn parts not allowing the pressure plate to release the clutch plate completely, or, some broken springs in the pressure plate.
Here is an exploded view of the clutch release mechanism of a 65 an newer 930 CK, on the Case/IH online parts store
Official Case IH Online Parts Store and Case IH Catalog for Best Parts Search and Best Parts Look Up. Case IH Parts for Case IH Tractors, Case IH Combines, Case IH Tractors, Case IH Manuals, Case IH Parts. It does not show a'63 model, other than a Wheatland model, so I'll assume this is similar to yours.
Looking at the exploded view, I'm seeing a couple items that could be a culprit. Parts 18, 19, and 25. Clutch release cross shaft, woodruff key, and clutch release bearing yoke. If the bolt clamping the clutch release lever has worked loose, it could possibly allow the woodruff key to become partially, or completely sheared off. Or, the yoke key way, or yoke itself could be worn enough to not function as it should.
If starting in gear, and applying the brakes kills the engine at low throttle, and clutch does not slip, I'd have to say you'll have to split it, and have a look inside.