What the help document is discussing is that when you use the 'table' option you will see the entries for the individual rasters and overviews in the Mosaic Dataset. Since you can see the individual rasters in the new mosaic dataset copy, those individual rasters can be removed, queried or had functions added to them individually. When you select the option to simply add the mosaic dataset directly as a raster dataset, then you will only see the reference to the original mosaic dataset.
To make a second mosaic dataset containing only a selection from the first, there are two options:
Using a Selection:
1. Add the first mosaic dataset to ArcMap.
2. Using the selection tool, select the footprints of the items you want to add the second mosaic dataset. Such as using the Select Features By Rectangle tool or opening the attribute table and making a selection in the table.
3. Open the Add Rasters To Mosaic Dataset tool.
4. Select the Table raster type.
5. Drag the mosaic dataset layer to the Source text box on the tool
6. Make any other relevant changes and run the tool.
Use a Query:
1. Open the Add Rasters To Mosaic Dataset tool.
2. Select the Table raster type.
3. Expand the Advanced Options.
4. In the File Filter parameter enter an SQL query. For example, if you want to ingest everything that has an ObjectID less that 5 type: OBJECTID < 5
5. Make any other relevant changes and run the tool.
