Outtasking means an exclusion of a task. The term is not used in practice very often, it is an alternative to outsourcing with which it quite blends. Earmarked task, activity or service are smaller the in the case of outsourcing. It can be talked about a kind of outsourcing in a smaller scale and usually in a greater degree of specialization.
An example of outtasking may be allocation of simple task application in a form of Software as a Service (SaaS).