Within HR you have the option to allow employees to edit and delete time off requests they have submitted in Self service 

Administration -> Company -> Settings -> Time off settings (Global)

In the 'Self service' section you will see two options available 'Allow employees to edit time off' and 'Allow employees to delete time off' shown below:

If either of these options are set to 'Yes' then your employees will be able to edit and/or delete their time off requests by navigating into:

Self-Service -> My requests -> Time Off

On this page, In addition to the View action, the employee will also see the 'Edit' and 'Delete' actions in the 'Actions' column.

To note 

If either of these options are set to no then the corresponding action will not be available to employees. It is important to note that Approver, Manager, HR and Admin level users will have the ability to edit and delete these instances on behalf of the user if required, regardless of both of these settings.

Also employees are only able to delete and edit time off that is in the booked or pending status, if a request is in the Taken status the employee will only be able to View the request and a admin or HR user will need to edit or delete the request for the employee