When the clutch is engaged, the engine-side springs compress to supply the torque and match the speed difference. When it's disengaged, the springs expand back out as it returns to engine speed. The obvious problem is that clutches do not smoothly click on and off like a transistor.
However there are more specialized devices that use stick-slip dynamics like piezo actuators. Since there is a much more rapid transition between "on"/"off", they can be very efficient and allow relatively weak devices to exert very large forces. They're just only able to take very small steps.
[1] Labeled 4 here: https://haynes.com/en-gb/sites/default/files/styles/blog_lan...