The pear tree was planted in Gretna Green in May to mark the 100th anniversary of the Quintinshill crash close to the Scottish-English border.
Police said it was cut down some time between Friday and Saturday, and described it as a “wanton act of vandalism”.
The rail disaster claimed the lives of more than 200 soldiers, most of whom came from in and around Edinburgh.
On 22 May 1915, a train packed with First World War troops travelling from Larbert, Stirlingshire, collided with a local passenger service near Gretna.
Straight afterwards, a Glasgow-bound express train smashed into the wreckage at the Quintinshill signal box, setting off a devastating fire which engulfed the troop train, packed with nearly 500 members of the Leith Battalion of the Royal Scots.
The troops were on their way to Liverpool, where they were due to sail to the frontline of the war in Gallipoli.
A series of events were staged in Edinburgh and Gretna earlier this year to mark the centenary.
First Minister Nicola Sturgeon and Princess Anne were among those attending a church service and wreath-laying ceremony in Gretna before the commemorative tree was planted.
PC Andy Aitken, of Police Scotland, said: “It beggars belief that someone has carried out such a wanton act of vandalism.
“We are keen to hear from anyone who may have seen or heard anything suspicious in the area of The Green at Gretna Green to get in touch through 101 if they can help.”
Earlier this year a senior retired army officer said some soldiers were “probably” shot in mercy killings after the disaster.
There are no official army accounts of the alleged shootings on the day of the crash.
But many reports at the time of the accident suggested some trapped soldiers, threatened with the prospect of being burnt alive, took their own lives or were shot by their officers.
These reports were long officially denied for lack of official reports.
Colonel Robert Watson, one of the most senior veterans of the Royal Scots, earlier this year told the makers of a BBC documentary – Quintinshill: Britain’s Deadliest Rail Disaster – it “probably” did happen in a very few case, “perhaps one or two”.
Col Watson said: “My own personal belief is that it probably did happen, in a sense of compassion, of mercy killing.
“It’s almost impossible, sitting here, to comprehend what it was like that morning.”