Do I use a semicolon correctly in this sentence?

"This caused David to become a spectator rather than a sufferer; covering his misery with mercy and sadness with compassion (3.2.4)."

No, a semicolon should not be used in this sentence. Semicolons are used to separate two independent clauses. The last half of your sentence is an adjective phrase, not a clause.

What mark of punctuation do you think should go after "sufferer?"

A comma?

Right. A comma should be placed after "sufferer." :-)

how should i now what form of the word to put in sentense

Yes, the semicolon is used correctly in the sentence you provided. It is used to separate two independent clauses that are closely related in meaning. In this case, the semicolon separates the two independent clauses "This caused David to become a spectator rather than a sufferer" and "covering his misery with mercy and sadness with compassion (3.2.4)." By using a semicolon, you are emphasizing the connection between the two ideas.