Vernon Scannell's verse A Case of Murder tells the tale of a nine-year-old who is left home alone with the family cat.
The child first hits the animal with a stick before killing it by slamming a door.
The poem's violent content has angered parents who do not think it suitable for children.
Celeste Cowley was shocked when her twin boys came home from Peebles High School with the poem and said she feared such violent literature could desensitise youngsters.
"It is a very dark poem which celebrates violence," she said. "My son said they were encouraged to draw pictures and some were drawing pictures of a cat being slammed in a door. I can't think of one parent who thinks this a good poem for children."
Fellow parent Jill Fraser agreed: "It's shocking, especially with so much in the news about animal cruelty. Everyone I've spoken to has been disgusted."
Nick Seaton, chairman of the Campaign for Real Education, called the poem "horrific" and added: "It will appeal to bullies and those with a cruel streak, and upset or de-sensitise normal children. And it may put ideas into their heads."
Ross Minett, campaigns director for Advocates for Animals, agreed that the poem was distressing. "Of course teachers must reinforce the message that any cruelty to animals is totally unacceptable," he said.
Judith Gillespie, policy development officer with the Scottish Parent Teacher Council, did not object to the violence. She said: "Unless you can isolate children from the news you cannot keep them from the violence of the world, particularly given the events in Gaza recently.
"But it does seem a rather complex poem for this age group."
Sue Palmer, author of Toxic Childhood and child development expert, backed use of the poem in the early years of secondary. The former headteacher said: "Children need to talk about, and come to terms with, the violence around them."
An education spokeswoman for Scottish Borders Council said the poem was taught to first-year pupils throughout Scotland. "It is even recommended by Moray House (education faculty at] Edinburgh University to trainee teachers as a poem very suitable for S1," she said. "In over 25 years of English teaching we have never had a parental complaint.
"The poem is in fact a very moral tale, focusing very much on the boy's terror, guilt and remorse following the accidental killing of the cat.
"Serious issues of this nature are routinely explored in English teaching at all levels."
However, a spokeswoman for Edinburgh University denied that its education faculty had ever recommended the poem.
She said: "It is not within the remit of the Moray House School of Education to advise on specific curriculum materials."
Celebration of violence or moral tale?
A Case Of Murder
He hated that cat; he watched it sit, A buzzing machine of soft black stuff, (...] So he took Daddy's stick and he hit the cat. (...]
Then quick as a sudden crack in glass
It hissed, black flash, to a hiding place
In the dust and dark beneath the couch,
And he followed the grin on his new-made face, A wide-eyed, frightened snarl of a grin, And he took the stick and he thrust it in, Hard and quick in the furry dark. The black fur squealed and he felt his skin. Prickle with sparks of dry delight.
Then the cat again came into sight, Shot for the door that wasn't quite shut, But the boy, quick too, slammed fast the door:
The cat, half-through, was cracked like a nut And the soft black thud was dumped on the floor.
Then the boy was suddenly terrified
And he bit his knuckles and cried and cried;
But he had to do something with the dead thing there.
His eyes squeezed beads of salty prayer
But the wound of fear gaped wide and raw;
He dared not touch the thing with his hands
So he fetched a spade and shovelled it
And dumped the load of heavy fur
In the spidery cupboard under the stair
Where it's been for years, and though it died
It's grown in that cupboard and its hot low purr
Grows slowly louder year by year:
There'll not be a corner for the boy to hide
When the cupboard swells and all sides split
And the huge black cat pads out of it.
These verses are extracts from the poem