As an alternative to using UsedRange or providing an explicit range address, the AutoFilter.Range property can also specify the affected range.
ActiveSheet.AutoFilter.Range.Offset(1,0).Rows.SpecialCells(xlCellTypeVisible).Delete(xlShiftUp)
As used here, Offset causes the first row after the AutoFilter range to also be deleted. In order to avoid that, I would try using .Resize() after .Offset().