Leikkaan juustosta ohuen viipaleen voileivälle.

Leikkaan is the 1st person singular present tense of leikata (to cut).

So it means:

• I cut
• I am cutting

Finnish present tense can cover both simple present and present continuous, and context tells you which is intended.

Because Finnish usually leaves out subject pronouns when the verb ending already shows who the subject is.

• Leikkaan = I cut / I am cutting
• Leikkaat = you cut
• Leikkaa = he/she/it cuts

So minä is not necessary here. You could say Minä leikkaan..., but that would usually add emphasis, contrast, or clarity.

The object is ohuen viipaleen (a thin slice).

That is the thing being cut.

The other case forms are not objects:

• juustosta = from the cheese → source
• voileivälle = onto/for the sandwich → destination/target

So the structure is roughly:

• Leikkaan = I cut
• juustosta = from the cheese
• ohuen viipaleen = a thin slice
• voileivälle = onto/for the sandwich

Juustosta is the elative case of juusto, with the ending -sta.

The elative often means out of or from. Here it marks the source: the slice is being cut from the cheese.

This is very natural Finnish with actions like taking or cutting a piece from a larger whole:

• leikata kakusta pala = cut a piece from the cake
• leikata juustosta viipale = cut a slice from the cheese

Yes, but it would not mean quite the same thing.

• Leikkaan juustoa = I am cutting cheese / some cheese

  • more general
  • focuses on the material being cut

• Leikkaan juustosta ohuen viipaleen = I cut a thin slice from the cheese

  • focuses on taking one slice out of a larger piece

So juustosta is better here because the sentence is about cutting a slice off/from the cheese.

Because viipaleen is the natural form for a singular total object here: one whole slice is being cut.

In Finnish, when the action has a clear result and the object is a complete, countable thing, Finnish often uses the total object. With ordinary singular nouns, that form usually looks like the genitive:

• viipale → viipaleen

So ohuen viipaleen suggests:

• one complete slice
• a bounded, result-oriented action

By contrast, viipaletta would be partitive and would make the action sound more unbounded, incomplete, or less result-focused.

Because adjectives must agree with the noun they modify.

The noun is viipaleen, so the adjective also takes the same case/number form:

• ohut viipale = a thin slice (nominative)
• ohuen viipaleen = a thin slice (as the total object here)

Also, ohut changes its stem in other forms:

• ohut
• ohuen
• ohutta

So this is both agreement and a normal stem change.

Voileivälle is the allative case of voileipä, with the ending -lle.

The allative often means:

• onto
• to
• for

Here it shows the destination or target of the slice: the slice is being cut for/onto the sandwich.

Because those two cases give different spatial ideas:

• -lle = onto / to / for
• -Vn (illative) = into

So:

• voileivälle = onto the sandwich / for the sandwich
• voileipään = into the sandwich

In Finnish, when food is placed on bread, -lle is very common:

• laitan voita leivälle = I put butter on the bread
• laitan juustoa voileivälle = I put cheese on the sandwich

So voileivälle is the natural choice here.

Because Finnish words often use a different stem when case endings are added.

Here:

• dictionary form: voileipä
• stem in many oblique cases: voileivä-
• allative ending: -lle

So:

• voileipä → voileivä- → voileivälle

This kind of consonant/stem alternation is very common in Finnish and is something learners gradually get used to.

Finnish does not have articles like English a/an and the.

That means Finnish often leaves it to context whether something is:

• indefinite: a thin slice
• definite: the thin slice

In this sentence, English would normally say a thin slice, because that sounds most natural out of context. But Finnish itself does not mark that distinction with an article.

Yes. Finnish word order is fairly flexible, because the case endings show the grammatical roles.

The original sentence is a neutral, natural order:

• Leikkaan juustosta ohuen viipaleen voileivälle.

But other orders are possible if you want different emphasis:

• Juustosta leikkaan ohuen viipaleen voileivälle.
  Emphasizes from the cheese.

• Voileivälle leikkaan juustosta ohuen viipaleen.
  Emphasizes the destination/target.

• Ohuen viipaleen leikkaan juustosta voileivälle.
  Emphasizes the thin slice.

The meaning stays basically the same, but the information focus changes.

They are:

• leikata = to cut
• juusto = cheese
• ohut = thin
• viipale = slice
• voileipä = sandwich / open sandwich

These are the forms you would usually look up in a dictionary.