Writing out PointM shapefiles from QGIS

You can use "Processing Toolbox > Vector Geometry > Drop M/Z Values" tool.

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As workaround, you could use a virtual layer, specifying a query similar to the following:

SELECT id, MakePointM(x, y, attribute) AS geometry FROM PointZM_layer;

And then export the virtual layer as a shapefile.

Please note: I didn't have the chance to test this! :)

Reference: https://docs.qgis.org/2.14/en/docs/user_manual/working_with_vector/virtual_layers.html

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