Spot on Sahir..;.but might I add a third option here? (kinda the same as option #1 but more explicit in configuration)
3. In your HCM P&F config, as mentioned have "approved_date" mapped to a generic service to set the value (sy-datum?)....it would be pretty basic. You would NOT assign this operation for use in any other form scenario steps. Set up your form scenario steps so that you have one...say "background" which includes all fields/operations...including your operation for the "set approved date". After your "approve" task in workflow (which Sahir rightly states will NOT trigger a "do_operations" , make your next step the standard "save in background" and assign it your form scenario step (which will set your approve date).