Do all GA autopilots use cable "clutches"?
From the Approval of Flight Guidance Systems AC-25-1239-1C document:


  30. Override of the FGS.
  
  
  a. General. An override of an engaged FGS function is defined as an action taken by the flightcrew intended to prevent, oppose, or alter an operation being conducted by the FGS function without first disengaging that function.
  
  b. Autopilot override.
  
  &nbsp;&nbsp;&nbsp;(1) With automatic disengagement.
  
  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (a) Override force. The autopilot should disengage when the flightcrew applies a significant override force to the controls. The applicant should interpret “significant” as a force that is consistent with an intention to overpower the autopilot by either or both pilots. The autopilot should not disengage by minor application of force to the controls, such as a pilot gently bumping the control column while entering or exiting a pilot seat during cruise.


(Page 37)

It goes on to say that 25lbs of force has been determined to be a significant override force level for "other than approach" operations. This may be difficult to measure using a system that just looks at the force on the control surface since normal operations may cause force feedback through the surface. There would have to be a way to measure the pilots force in conjunction with the control surface force and determine if the pilot is trying to override the servo.

GA aircraft are not normally equipped with all the "bells and whistles", autopilots are typically optional equipment. This means that the autopilot system needs to "fit in" to the existing control system architecture. Adding bosses, actuators, connection points, holes, etc to an airframe to accommodate an autopilot is a "significant modification" that may require a new type certificate or an STC.

The easiest way around this is to use servo controls with clutches that move existing control cables. This way the pilots force is directly measurable on the control system. Using magnetic clutches the autopilot can easily disconnect itself, worst case, by popping the autopilot breaker (although this is not an acceptable disconnection procedure). 

I can't say that there are no GA aircraft that don't use a different mechanism, but I've never heard of one.