If your vehicle is showing shuddering or vibrating when releasing the clutch, here are the most likely causes and the parts you'll need to fix each one.
Over time, the clutch friction material wears down or becomes glazed (smooth and shiny) from heat. This causes the disc to slip and grab unevenly as it tries to engage the flywheel.
Excessive heat from slipping the clutch can warp the flywheel or create hardened 'hot spots' on its surface. The clutch disc bounces over these imperfections, causing a severe vibration.
An engine oil leak from the rear main seal or a transmission fluid leak from the input shaft seal can coat the clutch disc. The fluid causes erratic slipping and grabbing during engagement.
Degraded or broken mounts allow the entire engine and transmission assembly to physically shake when torque is transferred to the drivetrain, mimicking an internal clutch shudder.
Failing to clean the anti-rust coating off a new flywheel, accidentally getting grease on the friction disc, or unevenly torquing the pressure plate bolts will cause immediate shuddering after a replacement.
The pilot bearing supports the tip of the transmission input shaft. If it fails, the shaft can wobble, causing the clutch disc to vibrate violently as it tries to center itself during engagement.