When you prune a tree, you create a wound. If you use the correct methods on a healthy tree, you don't need to worry. Tree sap, gums, and resins are the natural means by which trees combat invasion by pathogens. Although unsightly, sap flow from pruning wounds is not generally harmful; however, excessive "bleeding" can weaken trees.
TIP: "Always sterilize your pruning tools before using."
Oaks and Elms
When oaks or elms are wounded during a critical time of year (usually spring for oaks, or throughout the growing season for elms)--either from storms, other unforeseen mechanical wounds, or from necessary branch removals--some type of wound dressing should be applied to the wound. Do this immediately after the wound is created.
TIP: "To avoid injury, prune trees in winter when they are dormant."
In most other instances, wound dressings are unnecessary, and may even be detrimental. Wound dressings will not stop decay or cure infectious diseases. They may actually interfere with the protective benefits of tree gums and resins, and prevent wound surfaces from closing as quickly as they might under natural conditions. The only benefit of wound dressings is to prevent introduction of pathogens in the specific cases of Dutch elm disease and oak wilt.
TIP: "Before using a wound dressing or wound paint, check with your local Cooperative Extension Office regarding the prominence of specific disease in your area."
Courtesy of the US Dept. of Agriculture.