Cropping Shapefiles in QGIS?

You say you have a shapefile with appropriate regions, so you can use that for cutting. In the parlance of QGIS, it sounds like you are after Vector->Geoprocessing Tools -> Clip. If you need to assign the data from the input layer to smaller units in the region layer, you could intersect or union instead, in the same menu.

edit (by Kurt): here is an image for clarification: yellow: input layer (china) green: clipmask-layer violett: clipped output-layer

To create a new clip layer from scratch (In your case the rectangle).

Layer > New > New Shapefile layer (create blank vector object)

In layers menu: Right click on layer > toggle editing > use capture points, capture lines & capture polygons to create your customized new layer.