I finally found a solution by myself :-)

Firstly, bind the MinWidth of the popup with the Tag property of XamComboEditor by setting:

<Popup x:Name="Popup" Grid.ColumnSpan="2" IsOpen="False" VerticalAlignment="Bottom" >
                                    <Border x:Name="RootPopupElement"
                                            MinWidth="{Binding RelativeSource={RelativeSource TemplatedParent},Mode=OneWay,Path=Tag}" ....

Secondly, each time after xamComboEditor1.ItemsSource is set, investigate every item in the ItemsSource, find out how wide a textblock should be to show the whole content of the item and set the maximum of the item widthes to the Tag property of xamComboEditor1, as following:

        private void SetPopupMinWidth()
        {
            xamComboEditor1.Tag = null;
            List<string> items = xamComboEditor1.ItemsSource as List<string>;

            if (items == null)
            {
                return;
            }

            Thickness? padding = null;
            double? fontSize = null;
            double minWidth = 0;
            FontFamily fontFamily = null;

            //find the Padding/FontSize/FontSize value in ItemContainerStyle
            foreach (Setter setter in xamComboEditor1.ItemContainerStyle.Setters)
            {
                if (setter.Property == ComboEditorItemControl.PaddingProperty)
                {
                    padding = (Thickness)(setter.Value);
                }

                if (setter.Property == ComboEditorItemControl.FontSizeProperty)
                {
                    fontSize = (double)(setter.Value);
                }

                if (setter.Property == ComboEditorItemControl.FontSizeProperty)
                {
                    fontFamily = setter.Value as FontFamily;
                }
            }

            foreach (string item in items)
            {
                TextBlock tb = new TextBlock();
                tb.Text = item;

                if (padding != null)
                {
                    tb.Padding = padding.Value;
                }

                if (fontSize != null)
                {
                    tb.FontSize = fontSize.Value;
                }

                if (fontFamily != null)
                {
                    tb.FontFamily = fontFamily;
                }

                if (tb.ActualWidth + 20 > minWidth)
                {
                    //tb.ActualWidth is the minimal width to show the whole item content.
                    //20 is added for the width of vertical scroll bar of the popup.
                    minWidth = tb.ActualWidth + 20;
                }
            }

            xamComboEditor1.Tag = minWidth;
        }

By doing the above, the popup width is made dependent.