I think there is a place where you can control the distance of cut and the direction of the cut, I think it's a pain to do it that way, unless there are some enhancements that I don't know about.
What I do, is to add a configuration and add a cut extrude then you can control it......
When you do a broken out section you can choose certain components to not get cut. So one thing you could do is make the broken out section only cut the tube part and adjust the depth as necessary. To do this you go to the broken-out section properties and under the "Section Scope" tab you select the components that you want to remain uncut. You can select them in the tree if that is easier.
Another option is to do as John suggested and make the cut in the assembly with an extruded cut. In that case you can also control the feature scope to only cut certain components. But with that method you have the added flexibility that you could make the cut in a direction that is not normal to the drawing view. You could also add a hatch pattern manually to the cut surfaces in the drawing.