One way?

Sub SelectUsedRangeLessTopRow()
With ActiveSheet.UsedRange
mr = .Rows.Count
mc = .Columns.Count
       .Range(Cells(2, 1), Cells(mar, mc)).Select
End With
End Sub

A couple more:

   With ActiveSheet.UsedRange
       .Offset(1, 0).Resize(.Rows.Count - 1).Select
   End With

Or if you always wanted to select A2 through the lastusedcell:

   With ActiveSheet
       .Range("a2", .Cells.SpecialCells(xlCellTypeLastCell)).Select
   End With

There's a difference between these two.  The .usedrange doesn't have to start in
A1.

Try

With Worksheets(1).UsedRange
   .Cells(2, 1).Resize(.Rows.Count - 1, .Columns.Count).Select
End With