In the QI episode about killers the panel mentions that German SS soldiers during WWII were given puppies at the start of their training to raise, and then they were required to kill the dogs at the end of the training.
I found that the same claim was made about various armies and/or units: Iraqi, Israeli, American, Russian and others.
I found some references that the Bolivian army used dogs as live targets, but I couldn't find any credible sources reporting this, the most credible source was PETA, but I couldn't find the story in any large news outlet online even though Peta claim:
...the Bolivian minister of defense went on that country’s national television to announce an historic ban on all animal abuse in military training exercises, stating that the Bolivian government is issuing Resolution 217 to prohibit all acts of violence, exploitation, and mistreatment that provokes the death of animals.
And that post was published on April 1st, 2009.