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your slicer can handle this, there is a split function in most slicers, when you click on it the STL file is split into each of its components. and then you can delete the pieces you do not want.

another option is you can download meshmixer from autodesk which is free, load the STL then click edit and click seperate shells. then you can select the pieces you wish to export back into STL files. this will separate all the little groups of parts.