It is possible with formulas, or when you copy data, remove autofilter, and then paste, but I strongly advice against this in way how you want it. The user will see copied data correctly only then when there is no autofilter applied.

With formulas you can have a report on separate sheet. You select the "M" or "W" from data value list in some cell (at top of report) on report sheet, and according rows from data sheet are displayed. You can get an idea how this can be done from another response I wrote to another thread in same forum today (entries on your data sheet must be enumerated according the selection on report sheet).