Josh
This little macro will do that. I assumed your data starts in Row 2.
Sub ClearJM()
Dim LastRow As Long, LastJ As Long
Dim LastM As Long, rColN As Range
Dim i As Range, rJM As Range
Set rJM = Range("J1,M1")
LastJ = Range("J" & Rows.Count).End(xlUp).Row
LastM = Range("M" & Rows.Count).End(xlUp).Row
LastRow = Application.Max(LastJ, LastM)
Set rColN = Range("N2", Range("N" & LastRow))
For Each i In rColN
If IsEmpty(i.Value) Then
rJM.Offset(i.Row - 1).ClearContents
End If
Next i
End Sub