You can use the mobile application to overview the cases life cycle, complete tasks and other activities, however the basic mobile application tools do not allow to work with the approvals. We already had similar requests from different customers, therefore the functionality will be available in the future application releases.
Thank you parrett for giving information
You can include the "approval" detail in the record page and conditionally show/hide this i.e. you can show this approval detail only when the record is waiting approval. Hide it all the other time. This way we were able to include approval functionality in mobile app. You can read more on this here