Mapping Center Answer:

Unfortunately, the buffer and clip to shape workflow you are using doesn't provide a solution for eliminating the small road segments that don’t connect to the road network. This is possible if you use a page definition query. See the help topic for Using Page Definition Queries.

The page definition query allows you to set a definition query specifically for the current page. In this way you can control exactly what features show up on each page. To do this requires a little work though. You need to select the roads that you want for each page and code them with an attribute with the page name. You may want to make a copy of the roads for this because it requires adding an attribute and splitting them at the page boundaries. Once you have a copy you can use your index layer to split the roads and then select the roads that are contained in each index layer and calculate a page name attribute.