Sort by minimum value of two columns

NOT NULL columns. You need to add CASE expression into ORDER BY clause in following:

SELECT Id, Date1, Date2
FROM YourTable
ORDER BY CASE 
           WHEN Date1 < Date2 THEN Date1 
           ELSE Date2 
         END 

NULLABLE columns. As Zohar Peled wrote in comments if columns are nullable you could use ISNULL (but better to use COALESCE instead of ISNULL, because It’s ANSI SQL standard) in following:

SELECT Id, Date1, Date2
FROM YourTable
ORDER BY CASE 
           WHEN COALESCE(Date1, '1753-01-01') < COALESCE(Date2, '1753-01-01') THEN Date1 
           ELSE Date2 
         END

You can read about ANSI standard dateformat 1753-01-01 here.

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