Whenever you wish to cut out an image with the pen tool, this article will be of great help to you.
Begin by launching Illustrator CC and opening the image.
Go to Layers Panels on the right side. The first layer needs to be locked.
You can add another layer. Also, select the new layer.
Click the Fill and Stroke colors on the left toolbar and set them to None.
Select the Pen tool.
You are selecting the object you wish to cut by clicking around it.
Once the object is selected, click the starting point again.
Now, Unlock the first layer.
Then drag the red dot to the first layer.
Go to >> Select Menu and click All.
Go to >> Select Object Menu and click Clipping Mask and then Click Make.
You can export it as PNG with transparency.
All done! Here is the Final Result.