I have a polygon layer (pictured below) that I made by vectorizing a clip from the USDA Cropland Data Layer. The low resolution of the USDA layer causes fields that are separated by narrow roads to "bleed" into each other and be rendered as a single feature following vectorization.
For analysis purposes, I need separate fields to be rendered as separate features. So, I downloaded a vector roads layer and subtracted that from the crop layer, carving up the layer along the roads. I expected this to split bisected fields into separate features, but it did not, as shown below (only one side was selected, but both light up).
Manually splitting features one at a time is not an option. How can I use a geoprocessing approach to cut my crop layer along roads such that bisected features are split into separate features in the output? I'm using QGIS 2.8.