To be accurate, no curse was put on the monkey's paw. As noted above by bullgatortail, the sergeant-major simply said that a spell was put on it "to show that fate ruled people's lives."
After you finish reading the story, you might conclude that the spell was a curse, but that is only an interpretation based on lots of innuendo but flimsy evidence. The point of the story is that there really is no way to tell if the paw had any special power whatsoever.
Let's say it's true that Sergeant-Major Morris got the paw from a man whose last wish was for death. So what? We know nothing else about the other two wishes. Nor do we know about Sergeant-Major Morris's three wishes. We do know that he thinks the paw does a good deal of mischief, but he seems to be pretty healthy, even though he is a bit creeped out by and wary of the "unwholesome" paw.
And the White's experience when in possession of the paw is certainly harrowing and awful, but is the paw to blame? Who's to say that the paw caused Herbert's death, the windfall of cash, or a gruesome resurrection? There's simply no way to tell. And, again, that's the point of the story: Spell? Curse? Or just superstitious nonsense? Was it fate or a series of chance occurrences? There's simply no way to tell.
The evil talisman has a curse that follows all who possess it in W. W. Jacob's horror short story, "The Monkey's Paw." According to Sergeant-Major Morris,
"Well, it's just a bit of what you might call magic, perhaps," said the sergeant major offhandedly.
A holy man, "an old fakir," cast a spell upon the shriveled paw. His object: "To show that fate ruled people's lives." To interfere meant tempting fate and the wishes could be met with "sorrow." The spell dictated that three different men could have three wishes each. The sergeant major had already had his three wishes, and they had all come true. The first owner had used his wishes, too, and his third had been for death. In the end, the wishes came true, but never in the manner expected.