I have been unable to reproduce this issue. Objects should be moving in the direction of the axis arrow that click and drag. The part you are moving does have its X axis rotated in that direction, although the arrows in your screenshot appear to be oriented along the worldspace axes, so it shouldn't be moving diagonally like that. You can change whether manipulators (translate, rotate, scale) operate on a node's world space, local space or in the view space. You can double-check that your controls are using "World" space. See screenshot below:
If your problem is still not solved, a bit more information on the exact actions you took may be helpful.