Stimulating an axon causes impulses to travel both ways?
Allow me to do a silly analogy: think about the electric wire going from your outlet to your computer, conducting electricity. If you make two cuts in this wire, rotate it 180 degrees and weld it again at the cutting points, what will happen? It will conduct electricity just as it did before.

The same happens to an axon (but please have in mind that this is just an analogy, an action potential is not an electric current). That is, the axon doesn't determine or influence the direction of the action potential. If you cut a piece of that axon, rotate it 180 degrees and join it back in the cutting points, it will conduct the action potential the same way.

That being said, imagine that you stimulate that axon at a given point. There will be two action potentials, going to opposite ways: 


unmyelinated (A) and myelinated (B) nerve cells

In your figure (given that is a motor neuron), if you stimulate that axon in the middle, the action potential going to the neuromuscular junction, which is the normal direction, is called orthodromic (from the greek orthos, "proper", and edramon, past of "run"), while the one going to the soma (the perikaryon) is called antidromic (from the greek anti, "against").

According to Oh (2003):


  The sensory nerve conduction study measures the conduction of the nerve impulse along the sensory nerves. The routine method measures the conduction velocity of the large diameter sensory nerve fibers of the nerve being tested. There are two methods of obtaining sensory nerve action potentials (SNAP), orthodromic and antidromic. The orthodromic method includes recording of the sensory nerve action potential proximally and stimulating the nerve distally whereas in the antidromic method the location of the stimulating and recording electrodes is reversed. The latency and conduction velocities are identical with the orthodromic and antidromic methods if the recording and stimulating electrode positions are constant. (emphasis mine)


In a simplified scenario, the orthodromic impulse will reach the neuromuscular junction and stimulate the muscle contraction, while the antidromic impulse will be canceled by another orthodromic impulse or, if it can reach the dendrites, it will simply end, since there will be no neurotransmitter release.

Source: Oh, Shin J., 2002. Clinical Electromyography: Nerve Conduction Studies. Third. LWW.