You just need to put the rules in a list. Also, note use of RuleDelayed (:>
) which localises the variables x, y & z ensuring they don't pick up values from elsewhere in your program.
cleanAdjustedPoints[adjustedPoints_List] :=
adjustedPoints /. {{x_, y_, z_} /; x < 0 :> {0, y, z},
{x_, y_, z_} /; y > constB :> {x, constB, z}};
constB = 5;
cleanAdjustedPoints[{{-1, 2, 3}, {4, 5, 6}, {7, 8, 9}}]
{{0, 2, 3}, {4, 5, 6}, {7, 5, 9}}