Something like this should do.
procedure TForm1.Button1Click(Sender: TObject);
var
b:TBitmap;
begin
//lets copy a 100 by 100 pixels, at offset 100,100 from a TImage
b := TBitmap.Create;
try
b.Width := 100;
b.height := 100;
b.canvas.draw(-100,-100,image1.Picture.Graphic);
b.SaveToFile('d:\temp.bmp');
finally
b.free;
end;
end;