There are a variety of ways to remove pieces of a 3D object. The 3D Slice command has many methods (Slice by Line, Slice by Plane, Slice by (ACIS) Surface, Slice by Workplane and Slice by Facet). You can also create objects that surround the volume you want to remove and 3D Subtract.
It may even be useful to use the part of the object you want to keep as a template for creating a new (clean) object.
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