Once the 3D option is enabled on a layer, the Translate tool will work as a 3D Translate tool on that layer. This tool is able to move elements on all three axes.
You can click on the direction arrows to move your layer on only one axis. If you click anywhere else, the layer can move freely on two axes at once. Once the arrow is selected, it will turn pink.
NOTE If you move the layers in the Perspective view, it may be difficult to control the motion since you may not have the optimum point of view on your stage to understand the setup. In this case, it is best to use the direction arrows.