If the itemsSource is not within the datagrids itemssource you will have to find ancestor:
<DataGridComboBoxColumn itemsSource="{binding RelativeSource={RelativeSource ancestortype=Page}, path=DataContext.YourComboboxItemsSource}" />
Assuming your datagrid is on a page, you can change the ancestortype to anything. You can use relativeSource on anything though. The reason for having to use this is that the itemssource you are trying to set is not part of the hierarchy so it can't find it. Hope this helps.
MVVM I would do something like:
public list<string> ComboboxGridItemsSource { get; set; }
//Then add some data in the property above.
ComboboxGridItemsSource.add("Hello world1"); , ect...
And when this list gets altered/updated remember to raise the property using INotifyPropertyChanged.
//After you implement INotifyPropertyChanged you can raise like this:
RaiseProperty("ComboboxGridItemsSource");
Using MVVM you generally wouldn't manually set properties directly to the control but rather bind properties to that control in xaml.