You can only use -
on the numeric entries, so you can use decreasing and negate the ones you want in increasing order:
DT[order(x,-v,decreasing=TRUE),]
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