Can I route my form for approvals and have it approved by mobile?

Yes - you can.
Many business processes have to run through a series of approvals, from different people in the organization. Many companies run these processes manually - checking back and forth via phone calls, emails etc.
At FormTitan we provide an automated solution for such processes, which is called "Workflow". The workflow allows you to create a custom flow
in which your form advances. For example: when a form filler enters a certain information in your form you can have it sent to a designated person who will be required to approve or reject the step. once approved or rejected it will continue to follow the route you set. 
Read more about the workflow

As for approving via mobile - Once a form needs to be approved it is sent to the designated person via email, containing the data that was entered in it as well as an approval / rejection button. So you see...there is no problem approving via mobile. In addition, with FormTitan you can easily create responsive forms that may be filled in desktop mode, tablet and mobile, so in fact any part of the business process can be done in mobile.
Read all about creating responsive forms