Delete all data rows from an Excel table (apart from the first)

Your code can be narrowed down to

Sub DeleteTableRows(ByRef Table As ListObject)
    On Error Resume Next
    '~~> Clear Header Row `IF` it exists
    Table.DataBodyRange.Rows(1).ClearContents
    '~~> Delete all the other rows `IF `they exist
    Table.DataBodyRange.Offset(1, 0).Resize(Table.DataBodyRange.Rows.Count - 1, _
    Table.DataBodyRange.Columns.Count).Rows.Delete
    On Error GoTo 0
End Sub

Edit:

On a side note, I would add proper error handling if I need to intimate the user whether the first row or the other rows were deleted or not

I have 3 routines which work just fine, just select a cell in a table and run one of the subroutines

Sub ClearTable()
If Not ActiveCell.ListObject Is Nothing Then
    ActiveCell.ListObject.DataBodyRange.Rows.ClearContents
End If
End Sub

and Shrink Table to remove the databody range except from the headers and the first data row

Sub ShrinkTable()
If Not ActiveCell.ListObject Is Nothing Then
    ActiveCell.ListObject.DataBodyRange.Delete
End If
End Sub

and Delete Table to completely delete the table from the sheet

Sub DeleteTable()
If Not ActiveCell.ListObject Is Nothing Then
    ActiveCell.ListObject.Delete
End If
End Sub

This is how I clear the data:

Sub Macro3()
    With Sheet1.ListObjects("Table1")
        If Not .DataBodyRange Is Nothing Then
            .DataBodyRange.Delete
        End If
    End With
End Sub