Once you open the .png file in preview and crop the file to signature area

Select the Tools icon, then selection tool

And drag the tool over the signature so just that area is selected

Then Crop it

You should now have something like this

Now we remove the background using the magic wand tool

Click the tool , then drag it over a part of the background you wish to remove on the signature.

it will look like this

Hit the delete key on your keyboard.

If you still have prices of "background" simply use the maic wanf tool and repeat the process- drag/select an area and hit delete.

Save the File, and you your signature