Learn Finnish: Leikkaan leipää veitsellä.

Because bread is a mass noun and you are cutting an unspecified amount of it (some bread). Additionally, cutting is an ongoing action here. If you were cutting a whole specific loaf of bread and completing the action, you would use the accusative case: Leikkaan leivän.

What is the base form of leikkaan and why does it have a double k?

The base form (infinitive) is leikata (to cut). This is a Type 4 verb, which uses reverse consonant gradation. The infinitive has the weak grade (one k), while the conjugated forms, like the I form leikkaan, take the strong grade (two ks).

The ending -llä usually means on. Why is it used on veitsellä?

While the adessive case (-lla / -llä) often tells you location, Finnish also uses it to show what tool or instrument is used to do something. Here, it translates directly to doing something with a knife.

Why does veitsi become veitse- before adding the ending?

veitsi is an older Finnish word that ends in -i. In these older words, the final -i changes to an -e- before you attach most grammar endings. This gives the stem veitse-, making the final word veitsellä.