In general, the SplitButton is not part of the public API and does not provide suitable method that could be used to remove items from its menuButtons list dynamically. With the current implementation, the SplitButton is actually an inner widget of the ToolBar and its functionality is limited.
The SplitButton could be improved by defining it outside of the ToolBar scrope as a separate widget. Therefore, I have logged an enhancement task in the official Kendo UI GitHub repository for exposing the widget and improving the discussed functionality. You can start tracking the progress that we make on it from issue #4305
As an alternative, I would suggest integrating a Kendo UI DropDownList in the Toolbar as shown in the Basisc Usage Demo
. This way, you will be able to dynamically add/remove items from the DropDownList through the dataSource's add()