Overview of what we are going to do:
Create a Library.
Enable versioning.
Create a new View named Major.
Using SharePoint Designer, convert the Major View to an XSLT Data View.
Apply filtering to the Data View using the Approval Status field = Approved.
Save.
Using the same steps as above, create another View named Minor, and apply a filter for Draft.
Done.

Create a Document Library (I named my MajorMinor) and enable Versioning (Site Settings –> Versioning –> Create major and minor).

Create a new View and name it Major.

Once you have created your new Library, open SharePoint Designer, and open your site.

(File –> Open Site.. )

Now, navigate to your Library, open the Forms folder, and then open the Major.aspx page.

Once the page opens, right click on the Web Part and select Convert to XSLT Data View.

Right click in the Version field –> select Insert –> Column to the Right.

Now look in your Data Source Details Task Pane and locate the Approval Status field.  (If you don’t see the Data Source Details Task Pane, you will want to activate it from the Task Panes menu at the top of your screen)

Once you have located the Approval Status field, drag it into a cell of the column you just added to your Data View.

Now we are going to filter the Data View using our new field.

Click on the Web Part, select the little box in the top right corner of the Web Part, and then select Filter.

Click on Filter, once the Filter Criteria box opens, click on Click here to add a new clause….

From Field Name select Approval Status, Comparison should be Equals, Value is Approved, click Ok to apply the filter.

Save your page (click yes when the warning box opens).

Go back to your browser and refresh the page.  To test your changes, edit and save a document.

Now, to create your Minor View, use the same step shown above, but your filtered value would be Draft.

*NOTE*
1. If your Library has a Workflow attached, you will need to take into account the other Approval Statuses (Pending, Rejected, …)
2. You don’t need to add a new column to the Data View to use the filtering.  You could simply apply the filter without adding the column.