In WandaVision the SWORD members dismantle the body of Vision using some machines. As we know that his body is made up of vibranium I would like to know what metal is used to cut through vibranium.
We don't know what SWORD used when dissecting Vision's body and putting him back together a thousand times. However, vibranium isn't as strong as you state... though of course it is the strongest metal on Earth.
Leading with that it is only the strongest metal on Earth (Avengers: Age of Ultron) and we know that there are other metals that are stronger: Uru, for example, and also whatever Thanos' sword was made out of and Corvus Glaive's glaive. SWORD are also an organisation that exists outside of just Earth and works with at least the Skrulls, they clearly have access to some more advanced tech. It's not unfeasible that they could cut through vibranium.
Next we should note that Vision is not 100% vibranium, he was made from "wires and blood and bone". He was mixed with vibranium but also real tissue created from Helen's cradle.
Helen Cho: The Regeneration Cradle prints tissue; it can’t build a living body.
Ultron: It can, you can. You lacked the materials.
Avengers: Age of Ultron
Vibranium also has weaknesses, enough force from anything and it could penetrate it. Also as shown in Black Panther it is vulnerable to sonic based equipment such as Wakandan Maglev Train.
This is all of course ruling out whether or not they used more vibranium to cut through it which is a possibility as well with the Wakandans relationship with the Avengers and so likely SWORD now too. But in conclusion we don't know what was used to cut Vision up we just see a selection of hand tools being used or laying about.