Each tile exposes a set_selected(value, triggerEvents) method, as listed in their API reference: http://docs.telerik.com/devtools/aspnet-ajax/controls/tilelist/tiles/client-side-programming/basetile-object.
You can get all tiles from the tile list object through its get_allTiles() method: http://docs.telerik.com/devtools/aspnet-ajax/controls/tilelist/client-side-programming/tilelist-object.
Removing tiles is not allowed on the client because it will break the client state of the control and then the server code (control recreateion, viewstate loading, client state loading).
On the server, however, you can modify the tiles collections to match your needs. One of the easiest ways to do that is to data bind the tile list and modify the data source, then rebind it.
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