Follow the following steps:
1. create a new WorksheetPart
2. clone the existing worksheet's contents using XmlUtils.deepCopy; set the new worksheet's contents
3. use addTargetPart to add the part to the WorkbookPart
4. add the part to the list of parts in the workbook part (see xlsx-java-f15/how-to-remove-a-sheet-from-a-loaded-xlsx-template-t1027.html
That's all there is to it, if you aren't using shared strings and the source part doesn't reference other parts.