Dear Rockland,

Thank you for contacting us about the tree in your yard. I am not able to identify it from your photos. If you would send some closeups of the leaves and their arrangement on the twigs, I may be able to give you an answer. 

There are some protected trees in Oregon, but it is unlikely this would include yours without your knowing about it. I am not aware of any restrictions on removing a dead or dying tree from private property. You might call your municipality to confirm this with them.

Attached is a photo of the wooly beech aphid  (Phyllaphis fagi). You can compare it to the pests found on your tree.

There are many species of aphids. Some are generalists, but many are identified by host plant. If you search for images of beech trees, you might find that your tree is a beech. 

Here is some information about aphids in general:  
https://pnwhandbooks.org/insect/hort/nursery/common/nursery-crop-aphids

Chemicals are usually not necessary for aphid control as mentioned in the article. If you chooses to use horticultural soaps or oils, please note that they only work on contact with the pests body. Simply spraying leaves is not effective. 

I hope this information is helpful. Feel free to write again and let me know what you have found with regard to the pests and tree identity. 

Hi Lynne Marie. Thank you for your reply. I will send you the close ups of the leaves once they grow back, I just cut them back. Something of interest to note; when I trim the tree back, I don't see any evidence of aphids or any other bugs on the tree. I would think the little buggers would be crawling all over me. :)

Hello again,

Some aphids as well as scale insects do not move around much. They stay in their protective coverings. 

If you have removed all the leaves the tree cannot photosynthesize and it will eventually die completely. 

Thank you for your explanation.