Amber ooze on ornamental plum tree
mhWe viewed your photos. The tree looks like it has narrow crotch angles and does not have a good branch structure. There is branch dieback and the ooze may be from possible insect damage we cannot say for sure.
The ornamental plum is not a long lived tree in general. The tree will continue to limp along. If the tree is a hazard you should remove it. If it is providing some benefits such as shade, you can leave and remove once it has dropped its foliage.
Here is a helpful publication on When to Remove A Tree http://extension.umd.edu/node/2273