[Vuejs]-DataTables – Remove data from old table and initialise a new one

Sorry I post this as answer instead of comment, but my reputation is to low to post comments.

In jsfiddle you can use the fake ajax requests to emulate your call to your php backend.

Also is there a specific reason you are using jQuery DataTables? There is a very nice vue component which does the same (default with bootstrap styling, but you can style it as you like) https://github.com/matfish2/vue-tables

If you are loading the data via ajax, make your table ajax loaded. You will need to re-work the structure of your json response. Also see this.

From there, you can can call table.draw(); to reload it.