Blend file is hereIn the following picture I have a noise on a mesh, and a cylinder.
I want to cut the cylinder along the edges of the noise mesh.
I tried so many methods, nothing worked..
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Assuming your desired end result is a solid cylinder with a textured top surface, perhaps there is another approach. Rather than using a Boolean to create the base, which is likely to generate artifacts, and badly-behaved geometry here, you could start with the whole cylinder.
(To edit weights in Edit Mode, select a loop of vertices. In the Item > Vertex Weights panel, adjust the weight of the active vertex, and hit the button to copy the weight to the rest of the loop)
So now you can get control over the depth of your procedural displacement as it approaches the edge of the cylinder:
You can see a couple of slivers sticking up at the back right of this render.. you could adjust the weights in these areas to get rid of them. You can edit the weights in other ways, if you want to achieve a different effect.