You're going to need to give us a lot more detail and context to help with that question.
A good example of when I would like to change the rows and columns of an embedded visualization without going into the edit mode is when I am working with a pivot table and a large number of dimensions/measures. It really would be best if I could create a secondary application that could interact with the dragging and dropping of rows and columns and also give some more context to the fields that are being considered for on-grid, show a list of related fields, and to do so without the changing of gears involved with going into edit mode.
Is there a way to change the rows and columns without going into edit mode via the use of an API?
There is currently no way to programmatically change what is on columns/rows with any of our APIs. I am curious as to why you would want to do this with a secondary application when end users could just change what is on columns/rows themselves with web authoring. If that is not an option then you may be able to achieve something similar with parameters that show and hide values based on selections. Example: https://www.airweb.org/eAIR/techtips/Pages/Tableau-Dimensions.aspx.