Procedure GridRemoveColumn(StrGrid: TStringGrid; DelColumn: Integer);
Var Column: Integer;
begin
 If DelColumn <= StrGrid.ColCount then
 Begin
  For Column := DelColumn To StrGrid.ColCount-1 do
  StrGrid.Cols[Column-1].Assign(StrGrid.Cols[Column]);
  StrGrid.ColCount := StrGrid.ColCount-1;
 End;
end;

procedure RemoveColumn(SG : TStringGrid; ColNumber : integer);
var Column : integer;
begin
 ColNumber := abs(ColNumber);
 if ColNumber <= SG.ColCount then begin
  for Column := ColNumber to SG.ColCount - 2 do begin
  SG.Cols[Column].Assign(SG.Cols[Column + 1]);
  SG.Colwidths[Column] := SG.Colwidths[Column + 1];
  end;
  SG.ColCount := SG.ColCount - 1;
 end;
end;

procedure TForm1.Button3Click(Sender: TObject);
var
 i,j: Integer;
begin
 j:=SG1.Row; // строка с выделением
 SG1.Rows[j].Clear;
 for i:=j to SG1.RowCount-2 do
  SG1.Rows[i].Assign(SG1.Rows[i+1]);
 SG1.RowCount:=SG1.RowCount-1;
end;

type
  TStringGridHack = class(TStringGrid)
  public
  procedure DeleteCol(ACol: Longint);
  end;
 var
  Form1: TForm1;
 implementation

 procedure TStringGridHack.DeleteCol(ACol: Longint);
 begin
  if ACol = FixedCols then if ACol = (ColCount - 1) then
  begin
  Cols[ACol].Clear;
  if ColCount(FixedCols + 1) then ColCount := (ColCount - 1);
  end
  else
  begin
  Cols[ACol] := Cols[ACol + 1];
  DeleteCol(ACol + 1);
  end;
 end;