Tessellarius tesseras secat.

Because of the endings.

• tessellarius ends in -us, which here is a nominative singular ending. The nominative case is commonly used for the subject.
• tesseras ends in -as, which here is an accusative plural ending. The accusative case is commonly used for the direct object.

So Latin shows the job of each word mainly through case endings, not just word order.

Because tesseras is the accusative plural form of tessera.

The basic form is:

• tessera = one tile / one tessera

Its accusative forms are:

• tesseram = one tile, as a direct object
• tesseras = tiles, as a direct object

So the sentence means the worker cuts more than one tile.

Here are the cases:

• tessellarius: nominative singular
• tesseras: accusative plural

That gives us:

• who is doing the action? → tessellarius
• what is being cut? → tesseras

Secat is a verb form from seco, meaning I cut.

Here, secat is:

• present tense
• active voice
• indicative mood
• third person singular

So it means:

• he cuts
• she cuts
• it cuts

In this sentence, it matches tessellarius, which is singular.

Because Latin normally has no article.

English distinguishes between:

• the worker
• a worker

Latin usually does not make that distinction with a separate word. So tessellarius can mean either:

• the tessellarius
• a tessellarius
• the mosaic worker
• a mosaic worker

You decide from the context.

Yes. Latin word order is more flexible than English word order because the endings already show the grammar.

These could all express the same basic idea:

• Tessellarius tesseras secat.
• Tesseras tessellarius secat.
• Secat tessellarius tesseras.

The difference is usually one of emphasis or style, not basic meaning.

In your sentence, subject – object – verb is a very common and straightforward order.

They are:

• tessellarius, tessellarii = tessellarius / mosaic worker
• tessera, tesserae = tessera / tile
• seco, secare, secui, sectum = cut

Latin dictionaries usually list nouns with the nominative singular and genitive singular, and verbs with several principal parts.

• tessellarius is a second-declension masculine noun
• tessera is a first-declension feminine noun

That is why their endings look different:

tessellarius

• nominative singular: tessellarius
• accusative singular: tessellarium

tessera

• nominative singular: tessera
• accusative singular: tesseram
• accusative plural: tesseras

So tesseras fits exactly as the direct object plural form.

Grammatically, tessellarius is a masculine noun.

In many teaching sentences, that will naturally be translated as the male worker or simply the worker if gender is not important in English.

A corresponding feminine form would normally be tessellaria, if the context required a female worker.

Because the subject is singular.

• tessellarius = one worker
• therefore the verb is secat = cuts

If the subject were plural, the verb would also be plural. For example:

• Tessellarii tesseras secant.
• The tessellarii cut the tiles.

So Latin verbs agree with their subject in number and person.

A common classroom pronunciation would be roughly:

• tessellarius → tes-sel-LAR-ee-us
• tesseras → TES-seh-rahs
• secat → SEH-kat

In a more classical pronunciation, the c is always hard, like k.

So secat is seh-kat, never like English see-sat.

Also, the doubled ss and ll are really doubled in Latin spelling, even if many learners do not strongly pronounce the length difference at first.

Yes. Tesseras is just a different form of the same noun.

• tessera = the basic dictionary form
• tesseras = the accusative plural form

This is very normal in Latin: one word changes its ending depending on its role in the sentence.

So you should think:

• same word stem: tesser-
• different ending for different grammar: -a, -am, -ae, -as, and so on

A very literal breakdown is:

• Tessellarius = the tessellarius / the tile-worker as subject
• tesseras = tiles as direct object
• secat = cuts

So the structure is:

• [subject] [object] [verb]

or more mechanically:

• The worker tiles cuts

Then you turn that into natural English:

• The tessellarius cuts the tiles.
• or more idiomatically, depending on the vocabulary choice, The mosaic worker cuts the tiles.