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data.table v1.9.6+ now supports OP's original attempt and the following answer is no longer necessary.
You can use DT[order(-rank(x), y)].
DT[order(-rank(x), y)]
x y v 1: c 1 7 2: c 3 8 3: c 6 9 4: b 1 1 5: b 3 2 6: b 6 3 7: a 1 4 8: a 3 5 9: a 6 6