By default the menu will use the same 'duration' value as the button used. To let the menu auto hide when the mouse leaving it, try to set the 'duration' value when the menu displays.
<a href="#" class="easyui-splitbutton" data-options="menu:'#mm1',iconCls:'icon-edit',duration:99999999">Edit</a>
<div id="mm1" data-options="
onShow: function(){
$(this).menu('options').duration = 200;
}
">
<div>MenuItem1</div>
<div>MenuItem2</div>
<div>MenuItem3</div>
<div>MenuItem4</div>
</div>