Environmental Problems. There are a number of factors that may be to blame when a plum tree has sap oozing from trunk. Hot, dry conditions in summer or sunscald in winter can stress the tree and may be the cause for a plum tree oozing sap. The term "bleeding tree" is used to describe two different types of trees. Bleeding or oozing of sap from a tree, although not normal, won't necessarily permanently harm a tree or woody plant; most of them will survive.

They could be suffering from a disease called cytospora canker.

A small amount of sap dripping from a pruning cut does not harm a tree.
This sealant covers the wound, keeping it free from infection by insect or airborne illness. The amount of sap in the tree varies based on the time of year. Fruit trees leak sap for two main reasons: Borers have infested them.

So, wait until the spring or fall to prune any trees in your landscape that are dripping sap. Controlling these sources of damage will control gum deposits and sap flow, but there usually is no cure. Slime flux … Like the eucalyptus, the sap of this tree coagulates quickly with a blood-red color, but, unlike the eucalyptus, it is a type of latex. It’s recommended that you prune trees during the spring or fall. Disease

Once this happens, you will see a gray brown foamy liquid that is called slime flux. A eucalyptus tree oozing sap onto limbs or trunk is very likely a tree attacked by a long-horned borer insect.
A eucalyptus tree dripping sap is not a happy plant. It usually won’t kill the tree until bacteria starts to form. Most commonly peach, nectarine, plum or cherry trees ooze sap, but why? This plant is native to South American countries … When done during the summer or winter, pruning may stress the tree or even kill it. This isn't usually too much of an issue, but it's best to avoid it so you can prevent problems like gummosis and tree decline. The condition often indicates that the eucalyptus tree is under attack from a type of insect called the eucalyptus borer. Very few options exist for assisting the tree once it is attacked. Similarly, repeated overwatering can also weaken the tree and cause plum tree problems. If you make pruning cuts at that time, the tree may bleed sap. Dragon’s blood and bloodwood trees contain a red sap which, when the tree is cut, makes it appear as though a tree is bleeding. When you see a tree bleeding sap, you know there is a problem, and most likely it is bacterial wetwood. Fruit trees may ooze an amber-colored sap from a wound that is due to a disease called gummosis.