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I have two datasets of hundreds of polygons. Each has an ID and each ID appears exactly once in both data sets. One of each pair of IDs is bigger than the other but they always overlap somewhat. In the image, below, you can see such a pair in pink: the highlighted polygon is from data set 1 and the non-highlighted polygon is from data set 2. These are surrounded by other polygons that may or may not overlap them and have different IDs. I need to find a way to clip the polygons in dataset 2 only by the polygon in dataset 1 that has an identical ID such that, in the below case as an example, the only part of the pink polygons that is left is the spur extending to the bottom right.

 

I think, if I've understood correctly that you should be able to use an Area on Area Overlayer with a group by on the ID, then keep only those areas where the _overlaps attribute = 1

 

You may also be able to use a clipper, again with a group by on the ID and just using the output port, but i'm not sure from your description whether the polygon in dataset 2 is always bigger than the polygon in dataset 1

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