The Sandy Hook Elementary School killings on December 14 were one of the deadliest such shootings and led a push for tighter gun control laws in the United States.
A spokeswoman for the council in Newtown, Connecticut said the work would take up to five weeks and a new elementary school was expected to open in 2016.
"It started yesterday. The building itself will be demolished in pieces. The demolition will take four to five weeks," she told AFP.
Adam Lanza, 20, took just five minutes to shoot his way into the school, murder his victims and kill himself.
