Book about a time-traveling dinosaur hunter

You seem to be describing A Sound of Thunder by Ray Bradbury.

It has time traveling hunters tracking down a T-Rex. They travel on a special path to avoid contaminating the timeline. One of them goes off and messes things up.

The points that don't match is the 'some trouble and some die'. The 'disk shaped platform' rather than a 'path' and the 'only the head remains' with the trophy. That said, there have been multiple adaptations of it (comic book for example) that could have changed some of the specifics of the original story.

You can read it at Scary For Kids that also contains some frames of a comic book version.

This might be David Gerrold's novel "Deathbeast" (1981, a little later than what you remember, but very close)

The plot has two guides leading a party of hunters and photographers on a disc-shaped time travel device to the late Cretaceous to hunt dinosaurs. They're attacked very soon after arriving by a massive Tyrannosaurus, which slaughters a third of the party and escapes after being heavily wounded. One of the hunters insists on tracking it, and a sort of Ahab vs. Moby Dick situation develops between the humans - some of whom only want to go home - and the pain-maddened dinosaur. There is lots of description about their computerized tracking devices and the weapons, which use a sort of heat beam to cook the dinosaurs alive from the inside out. The novels ends with a scene just like you describe, with the battered few humans racing the dinosaur back to their time-travel platform, and managing to kill is just as it collapses on them.

Sounds like one or more of the Time Safari stories by David Drake.

Henry Vickers's job is to keep clients safe from the dinosaurs they're hunting. That's the easy part. The hard part is to keep the clients safe from themselves and each other. Men with enough money to go into the past to hunt the largest land animals of all time are powerful and self-willed. Some make an effort to act like decent human beings, but more are selfish, stupid, sadistic--or all three together. The few women are likely to be worse.

Vickers doesn't expect rich people to understand the dangers of where they are and what they're doing; he doesn't expect them to be competent with the powerful rifles they carry; and he particularly doesn't expect them to be reasonable. He treats his clients' behavior as he does the rain and the baking heat--the cost of having a life he loves and which he couldn't afford in any other way.

But no matter how detached Vickers tries to be, eventually there are moral questions that he can't ignore. And when Henry Vickers starts to behave like a human being instead of a hunting guide, things get really dangerous.