This looks like Phomopsis or Kabatina twig canker. Blue Points are notorious for dying back that way. Courtesy photo. In theory it's possible to dig up and transfer Asian jasmine to a new site.

Phomopsis sp. KS-37-2 was cultivated on sterilized, unpolished rice (20 g/Petri dish × 50) at 25 °C for 3 weeks. The moldy, unpolished rice was extracted with MeOH, and the MeOH extract was ...

Phomopsis Gall on Forsythia. Both are common pests in our area that might catch your attention but are nothing to worry about. There are several hundred insects, mites and fungi that cause ...