While the first known description of a surgical knife comes from the great greek physician Hippocrates, evidence of the use of blades in medicine have been found from as far back as the Mesolithic period about 10,000 years ago. And the modern scalpel isn't really all that different from the "macairion" that Hippocrates described. The fundamental features - a handle, a cutting blade on a single edge and a sharp, straight point at the end - remain unchanged.
Early Egyptian surgical instruments.
Indeed, the scalpel has evoled remarkably little in over 10 millenia of use. What has evolved tremendously, however, is the way that modern medicine uses this simple but powerful tool. Most of the known history of the scalpel - or any blade - in medicine is, for lack of a better word, barbaric. The earliest known cases involved using flint knives to bores holes into the skull, the belief being that this would "let out" whatever was making someone ill. Even just a few hundred years ago during the Dark Ages, "blood letting" was a common medical practice. Thankfully, today the scalpel is used much more conservatively.
To the extent that the scalpel itself has evolved, it's evolution closely follows the evolution of blades & cutlery in general. For surgical blades in particular, the primary concern of this evolution has been sharpness. The sharper a blade is, the clean and more precise a cut it can make. Of course that isn't the only concern - there's also the blade's shape, balance, rigidity and overall reliability.
1800's Spanish surgical kit.
The surgical scalpel as we know it today features a specialize handles with an interchangeable blade made from modern stainless steel alloys. This concept was inspired by the disposable shaving blades developed by King Gillette in the early 1900's. In 1910, Dr John B. Murphy of Chicago perfected the specialized handle and in 1915 Morgan Parker made the combination technically efficient when he found an ideal way to join the blade & the handle. Over the past few decades there have been additional adaptations and refinements, but the specialized handle and disposable blade design that was perfected nearly a century ago remains largley unchanged.
The scalpel is a unique case of the evolution of modern technology. Unlike other fundamental early inventions like the wheel, which gave us our earliest modes of transportation and paved the way for the bicycle and eventually the automobile, the scalpel is only still essentially just a blade. Yet it's history is just as rich, and despite over 10,000 years of refinement mankind continues to find new ways to improve not only the tool, but the skill with which it is wielded.
An assortment of modern surgical scalpels.