A family of Microsoft word processing software products for creating web, email, and print documents.
You can get this done in PowerPoint, then insert the result in Word.
In PowerPoint, convert the SmartArt to shapes using the SmartArt Design>Convert>Convert to Shapes command. Or draw your circles using Insert>Shapes. Overlap 2 circles, then copy and paste those and move them over top of the original shapes. Use Shape Format>Merge Shapes>Intersect. All parts of the circles are deleted except for the area where they overlapped. Color that as you wish to show the overlapping part.
If necessary, align the copies of circles with the merged shape, so it looks like a Venn diagram. Select all the shapes, right-click and choose Save as Picture. EMF format is probably good for your purposes, it's a vector format that can resized without it getting blurry. Then import the graphic into your Word document.
Here is Microsoft's page with more detail about using Merge Shapes.