At the base of the slip where it connects to the potato. If you look closely you’ll see roots in the area too. Just carefully cut a plug of potato with slip and root.

If you get the root with it you can skip putting the slip in water first to root and just plant it. Alternatively you can just plant the whole potato if you are not planning on planting a lot of potatoes.

Separating the slips is only useful when you plan on planting a few rows or selling them. (Sweet potato slips go for ridiculous prices online)

If you’re just planting a pot or two just use the whole potato. The slips will grow super fast pulling sugar and nutrients from the potato to jump start.