gistfile1.txt

grid = QgsMapLayerRegistry.instance().mapLayersByName('grid10')[0]
regions = QgsMapLayerRegistry.instance().mapLayersByName('Polygon_GADM_Brazil')[0]
points = QgsMapLayerRegistry.instance().mapLayersByName('Point_Population_Brazil')[0]

region_count = regions.featureCount()
cell_count = grid.featureCount()

shape_writer = QgsVectorFileWriter(
            '/tmp/out.shp',
            'UTF-8',
            regions.dataProvider().fields(),
            regions.dataProvider().geometryType(),
            regions.dataProvider().crs())

feat = QgsFeature()
for region_idx, region in enumerate(regions.getFeatures()):
    print 'Region %s of %s' % (region_idx + 1, region_count)
    
    region_geom = region.geometry()
    request=QgsFeatureRequest()
    request.setFilterRect(region_geom.boundingBox())

    for cell_idx, cell in enumerate(grid.getFeatures(request)):
        print 'Cell %s of %s' % (cell_idx + 1, cell_count)
        cell_geom = cell.geometry()
        intersection = cell_geom.intersection(region_geom)
        intersection_geometry = QgsGeometry(intersection)
        if intersection_geometry.wkbType() != 0:
            feat.setGeometry(intersection_geometry)
            shape_writer.addFeature(feat)
            
    del shape_writer