To kill the Buddha, to kill the Buddha. An oft repeated phrase, some call it a koan, but what means? Important first to understand that it situates itself within the Chan/Zen lineage of Buddhism, the line of Bodhidharma.
To understand what is meant here by 'Buddha' we must understand Bodhidharma's Buddhism. Within this special branch of Buddhism, the idea of 'Buddha' is played with tremendously, many koans revolve around "What is a Buddha", and these all have varying levels of koanic and serious answers. Most of them revolve on either the paradox of nirvana and samsara being one yet differentiated, but also on the idea of everything being the mind, and thus, the Buddha is the mind too. It must be understood that at this point in Buddhist history there is the concept of the Tathagatagarbha, the 'Inner Buddha', which for ease of explanation can be considered essentially the same as the Vedic atman, or just in English, the human soul. Yet neither of those capture it fully, and may lead one to misunderstand, if you want to get a better picture, I recommend reading the Tathagatagarbha Sutra yourself.
The whole point of Bodhidharmic Buddhism, or Chan/Zen is a radical acceptance of upaya, skillful means, most famously discussed in the burning house parable of the Lotus Sutra, but taken to its furthest possible conclusion here. If a house is burning, this is your mind, and you tell someone a lie to leave the burning house, is it a lie if they would have burned to death without the lie? In Buddhism the answer is no, this is not a lie, this is skillful means, it is compassion. Maybe this is horrifying to Christians who value objectivity, but this is not a concern in Mahayana Buddhism.
So to kill the Buddha we must ask first. What is the Buddha? Chan masters tell us quite simply, the Buddha is not Siddhartha Gotama the Shakyamuni, no he simply was the first to become enlightened in this era AND spread the message on how. So what is the Buddha? It is the mind. Okay, what is the mind? Everything. In Buddhism the entire universe is considered to be like a near eternal fire, always burning, always transmuting, always changing, yet all born from the first spark. This is why keen Buddhist scholars who become Buddhist see very easy and obvious parallels with Panpsychicism and Animism, because Mahayana, especially Chan, is essentially Animist in this regard.
If you are on the road, what is the road? The road is the path, the pay, the river that must be crossed. Upaya is the boat that gets you to the other side. You discard it when you reach the other side, yet on the other side you realize you need to help others get there, so once again you take up the boat once more. You tell people, "this boat will save you" yet it was not the "boat" that saved them, it was crossing the shore, which was made possible by the boat and the compassionate being who guided them (we call these people Bodhisattvas).
So now imagine the kind of society that Buddhism inhabits during this time. People are praying to the Buddha like he is God, they worship him, they lose sight of the practice, they believe that the boat -is salvation-. This is super important to understanding the phrase, and it has quite a lot of relevance to this day and age as well, and other religions. Think of this flipped, "If you see Christ on the road to Jerusalem, crucify him". This should make perfect sense, because even though Jesus is the savior, without his sacrifice his duty would not have been fulfilled, not only that, but we would be unsaved. Yet even then, this does not explain the koan completely, as Jesus is considered an actual savior human (or at least seemed human-like) figure, while Buddha is much more complicated.
So. If you see the Buddha on the road kill him. I will summarize it like this: If you are practicing Buddhism which is not a religion but simply the natural way of the mind (this is what Mahayana Buddhists believe), and you see the Buddha impede you on this road towards enlightenment, you are not meant to leave your wagon and get on your knees and pray, you are meant to carry on, thereby 'killing the Buddha'. The Buddha is that which removes obstacles, not which creates them. Thus it cannot be the true Buddha, so you must kill him. Any fruit that is sweet is considered the fruit of the Buddha, this is essential in understanding Buddhist epistemology. This is why you must kill the Buddha, because the Buddha is also empty, just like everything else. And emptiness is the Buddha, because Buddha is the mind, which is emptiness. Did Gotama need the Buddha to become the Buddha, the answer is no, so neither do you.