A family of Microsoft relational database management systems designed for ease of use.
The step of creating links between the drawing and a data source adds individual Shape Data fields to each linked shape. These are permanent fields, and do not disappear because the data links are removed, as you have noticed.
One option you can consider is to apply a Shape Data Set to the shapes in the drawing. You can use a shape with the desired Shape Data fields defined (and without the extra fields) as a 'template' to create a Shape Data Set. Then you can apply that Set to other shapes as needed in the same drawing.
The first step will be to capture a set from a normal Organization Chart drawing. Launch a new, blank Org Chart and place a shape (such as Position or Manager) on the page. Keep this drawing open while you open your existing drawing. Then copy the 'clean' shape from the new drawing into the existing drawing. You can then close the created blank drawing.
Select the copied shape, and View the Shape Data Window (View > Shape Data Window). You should see the existing data fields expected in a clean Org Chart object. To access the tools for managing Shape Data Sets, place your cursor in a part of the Shape Data Window that is below the fields. (Note: you may have to resize it to accomplish this). Right-click in this open area to see the options - and select the 'Shape Data Sets' option.
Make sure that your clean Org Chart shape is still selected in the drawing, and then select the "Add..." function in the Shape Data Sets window. Type a name for the set (something like Org), and make sure that the option "Create a new set form the shape selected in Visio" is selected, and click OK. This will create a set of data fields for use on other shapes.
Now that you have a set to use, select the shapes in your Org Chart diagram that you need to revert to basic fields. You will probably NOT want to select connectors, so using the Shift-Click feature will be useful to multi-select boxes. Also, you may want to move through the drawing in sections, rather than try to hit every shape on the page at once, but it is your choice. Once you have some shapes selected and are ready, you can put a check mark next to the defined set "Org" (or whatever you named it) and choose to apply to "Shapes selected in drawing", then click Apply.
Note: There is an option 'Remove existing data sets', which is normally on. This is a good feature, because you want Visio to essentially wipe the slate, and cleanly apply the set, without leaving other fields behind.
Once you have the drawing cleaned up, you may want to save it in Unlinked mode as a sort of template for later use :-)
Hope that helps!
Barb