As a short answer, you cannot do this. The cylinder for Clip is infinite. You cannot specify a fixed-length height.
The straightforward way to clip a limited-depth cylinder is to use a combination of cylinder and plane clips. Here is an example of using a Clip to get the data below the Z=3 plane, another to get the data above the Z=3 plane, and a third Clip that removes the cylinder from the upper clipped data.
clip-finite-cylinder.pvsm (706.7 KB)
The disadvantage of this approach is that the cells at the Z=3 plane all get split into 2.
There is some limited support to clip on arbitrary surfaces: Slice/Clip with a surface. You could potentially create a Cylinder source and use that for the clip. But the results do not always look great. In particular, I would expect that you would not see a nice right-angled clip at the base of the cylindrical hole.