According to your description, there is an Excel Web Access Web Part displays an Excel report in your site, you want to update the slice in this Excel report with
the data retrieve from SharePoint.
Excel Web Service is a good option to manipulate Excel files which is saved in SharePoint library, however, there is no such method in the exposed APIs in Excel Services
can meet this requirement:
As a workaround, I suggest you write code in the server side to download the Excel report to local drive, update it using Office API. For about getting project names
from SharePoint, SharePoint Object Model would be a good choice. Then upload and override the original version in a SharePoint library, you will be able to see a new version of Excel report in the Excel Web Access Web Part.
About how to access SharePoint using SharePoint Object Model, the links below would be helpful:
Add, Update and Delete List Items Programmatically in SharePoint
More information about
SharePoint Object Model:
About Programming with Slicers in Excel 2010:
If there would be more questions about how to work with slicer in Excel using Office API, I suggest you post it to the corresponding forum, you will get more help
and confirmed answers there.
The reason why we recommend posting appropriately is you will get the most qualified pool of respondents, and other partners who read the forums regularly can either
share their knowledge or learn from your interaction with us.