If you don't mind clarifying, what other Revolutions in this period are you comparing the French Revolution to? Both the American Revolution and Haitian Revolution had their fair shares of bloodshed.

The killing of the King is understandable because he is a symbol of the old way of government. Even killing the highest, most elite of the government was understandable. But killing every last government associate and even priests seems like a very noticeable turn from the traditional Enlightenment philosophies of Jean-Jacques and Voltaire.

Well, first of all, this never happened.

Second of all, we can have a look at the reasons people died during the Revolution. These numbers aren't exact, but:

Deaths from war with other countries: 290 000

Local deaths (civilian or fighters) from the civil war in the Vendée: 180 000

Revolutionary forces killed in the Vendée: 87 000

Deaths from other civil war: 35 000

Extralegal executions: 30 000

Jacobins killed in the counterrevolution in southern France: 14 600

Guillotined: 13 800

Deaths from starvation, etc: 7000

Add to that the fact that half of all those who were guillotined were armed rebels executed for taking part in the civil war in the Vendée. 2600 of the executions were in Paris, the rest were in the parts of the country that were somehow touched by war, civil or otherwise. Compare this map of the counterrevolution to this map showing where executions happened. (taken from Donald Greer's The Incidence of the Terror during the French Revolution)

As you can see, the overwhelming majority of all deaths were because of war. The executions were mostly related to the wars, and not something that people did for fun.

I will preface this with one thing. I cannot talk about the Haitian Revolution, the Revolutions in Latin America, and anything else that I'm missing.

The French Revolution is bloody only because of one thing, the power shifted completely. Within four years, power changed from the Absolutist Louis XVI whom ruled with general absolute power in France to the Committee for Public Safety ruled by twelve, with Maximilian Robespierre as it's head. Two very different types of government with Louis being the Second Estate and Robespierre being from the Third.

The French Revolution had started as one thing, a moderate Revolution where the middle class tried to force the Second Estate into allowing the Third Estate the right of political involvement not based on birth. The very beginning of the French Revolution, the Tennis Court Oath started because the Second Estate conspired to prevent proper representation of the Third Estate in the Estates General. It would continue as the new National Assembly would force a Constitution onto Louis through political manipulation of the Estates general.

This moderate, middle class revolution would fall apart due to one thing, Paris. The people of Paris slowly grew more and more angry during the French Revolution. The Storming of the Bastille is one act of many where the Parisian people forced their will on the Revolution, and did it with excessive force, where the governor of the Bastille was beheaded simply for being the governor. It would slowly build higher and higher with various acts of violence during the Women's March on Versailles, the storming of the Tulleries, and eventually the near general demand that Paris had on the death of Louis Capet.

It has reason, Paris was angry. It all comes down to anger. With excessive decadence in the face of the starving and destitute, the people of France wanted revenge on the nobility for their exploitative decadence. By co-opting the Revolution, the people of Paris were able to push the Revolution their way. It would be their Revolution after the proclamation of the Republic.

To take advantage of this, you had people like Marat. Marat acted to throw anything that would propel the Revolution. He wanted to push the French Revolution forward but did so in a bloody manner, through the media (back then papers and pamphlets), he would take names and publish supposed enemies of the Republic. This would in turn help propel the bloodshed of the Committee and the guillotine. It would take Charlotte Corday to stop his calls for the death of the enemies of the state.

However, the reason why this fear existed was that there was a fear of enemies of the state. Acts such as Louis flight to Varennes didn't help since he claimed to be a supporter of the Revolution yet turned around and lied. The French people were afraid and this Revolution was unlike anything else. The American Revolution was a moderate Revolution that created a new government, but the French Revolution aimed to completely change the society and culture of France as well as exporting it. They wanted to protect it and were afraid of it being over thrown.

Sources:

Twelve Who Ruled by R. R. Palmer & Isser Woloch

Liberty: The Lives and Times of Six Women in Revolutionary France by Lucy Moore