Currently, there is no way to add a new taxonomy term (catalog category, product attribute...) from the add product form.

We would ideally have :

  1. A link under each taxonomy reference field to add new one that will redirect to the add new term page on the corresponding vocabulary
  2. Redirect the user to the same form with the list up to date displaying the new term

There might exist some modules that handle that feature.

Files: 
CommentFileSizeAuthor
Product catalog references39.69 KBGuGuss
Product attributes44.43 KBGuGuss

Comments

We can't really use the autocompletion field to create new terms since some vocabularies need additional fields (i.e. : color needs an hexadecimal field)

1. is this a feature request or a support request?
2. this should be covered by Inline Entity Form module. At this moment IEF doesn't support Term reference field.
But there's a patch for this : #1659586-12: support taxonomy term ref field.