All the studies claiming to make these links have been comprehensively debunked. And it's worth remembering that the vast, vast bulk of fats and cholesterol in your body are not dietary, they were produced inside your body from other macro-nutrients. And they are essential. Without them you would die.
On a very basic level, blood flow gets blocked because inflammation in your arteries causes cholesterol manufactured by your liver to stick to the walls and build up. Consuming saturated fat does not cause this inflammation. Whereas there is evidence that consuming sugar does.