There are two ways I can think of that you could accomplish this.

First, for the document type containing the web part, create a custom field called, for instance, SearchResultText, and set that as the search content field. With this set, only the content of that custom field will show up in the search results preview. (Site Manager -> Development -> <Your Document Type> -> Search Fields)

Otherwise, you could create a custom function to filter out the content of the web part, based on specific text within the web part or other criteria. Under the Root document type transformations, modify SmartSearchResults and SmartSearchResultsWithImages so that results of the call to GetSearchedContent are passed through your custom function.

Regards,
Allen Greenhaw