There are two stories about the origin of this word, both from 19th-century France. The one thing that we can be certain of is that it had something to do with shoes.
If you visit Switzerland, you might buy wooden clogs as souvenirs today. Back in the 19th century, it was the preferred footwear across that part of Europe. French workers from rural areas used to wear wooden clogs routinely. In French the wooden clog is called Sabot.
In 1801, Jean Marie Jacquard invented the Jacquard Loom which was operated by punch cards. This made it possible for unqualified tradesmen to weave cloth. This also significantly sped up the production of cloth and thus put a lot of textile workers out of jobs. The unemployed textile workers were upset with the loom. They would routinely throw their shoes into the loom to disrupt the machine so that they would be given their jobs back. This action of disrupting the production of cloth came to be known as sabotage because it was the sabot that was being thrown into the machine.
The competing story also has to do with the textile industry. To this day, France is famous for its strikes. It is believed that textile mill owners would import rural hands to fill their mills to replace workers who went on strike. The rural hands would wear wooden clogs or Sabot. Since these temporary workers were not well trained they would slow down the production and also deliver poor results. These workers were derogatorily referred to as ‘Sabots’. Also watching the output suffer many of the workers came up with the idea that they could have their demands met without the risk of losing their jobs simply by working like the ‘Sabots’ rather than going on a strike. From this act of disobedience was born the word Sabotage.
Interestingly, the wooden clogs being thrown into machines is how the expression “clog up” comes.