A solution using the PyQGIS.
Let's assume there is a point layer called 'random_points_test' with its corresponding attribute table, see image below
Do not forget to change the layer and field names at the bottom of the code, i.e. split_layer('CMillor_ldcRefAuto_2013_WGSUTMH31','Fecha')
Proceed with Plugins > Python Console > Show Editor > New ...