I had a similar issue recently trying to clip and export a point shapefile to import into PostGIS. Shapefile was PointZM/Multipoint and I could clip but not export (ogr2ogr failed). These steps ended up working but I can't say why:

- Export original shapefile by explicitly selecting "Geometry" in the Export menu as Point and select "Force Multipoint" but make sure "Preserve Z-coordinates" is unselected to get rid of the Z values

- Export the new shapefile by the same process but unselect "Force to Multipoint" (and "Perserve Z-coordinates") to create a Point layer

This gave me a successful shapefile export that I was able to import into PostGIS.