Learn Swedish: Han klipper alltid tyget med saxen själv. - He always cuts the fabric with the scissors himself.

In Swedish, med is used to show how or with what tool an action is performed. Just like in English, med acts as an instrumental preposition to introduce the physical tool used for a task, which in this case is the scissors.

Could I use skär instead of klipper for 'cuts'?

No, because klipper specifically means cutting with scissors or shears. If he were cutting the fabric with a knife, you would use skär. Since he is using saxen (the scissors), the verb must be klipper.

English uses the plural 'the scissors'. Why is saxen singular here?

In Swedish, a single pair of scissors is a singular noun: en sax. To say 'the scissors' when referring to one tool, you use the singular definite form saxen. If you were talking about multiple pairs of scissors, you would use the plural saxarna.

Why does alltid come right after klipper?

This is a quick reminder of the V2 (verb-second) rule! In a main clause, the finite verb (klipper) must take the second position. Sentence adverbs like alltid generally follow immediately after the verb when the subject starts the sentence.