Learn French: Ce sont mes dessins, nous pouvons les découper. - These are my drawings, we can cut them out.

This sentence has a conjugated verb (pouvons) followed by an infinitive (découper). When this happens, the object pronoun (les) almost always goes right before the infinitive it logically belongs to. Since we are cutting them out, les is placed right before découper.

Why does the sentence start with ce sont instead of c'est?

Because the noun being introduced is plural. C'est means 'it is' or 'this is' for singular things (like c'est mon dessin). Since there are multiple drawings (mes dessins), we use the plural form ce sont (these are).

What is the difference between couper and découper?

Couper generally means 'to cut' in a basic sense, like slicing bread or cutting a string. Découper means 'to cut out' or 'to cut into pieces', which makes perfect sense here because the speaker is talking about cutting shapes or images out of paper.

Would les change if the word for drawings was feminine?

No. Les is the plural direct object pronoun for 'them', and it is used for both masculine and feminine plural nouns. It replaces mes dessins here, but it would stay exactly the same if it replaced a feminine plural word.