また means “again”.
つまらぬ is an old-fashioned and classical way of saying つまらない meaning “worthless”. Goemon often speaks in this old-fashioned way because he has a samurai spirit.
物 means “a thing” or “an object”.
The particle を is used to indicate what comes before is the direct object of the verb. So in this sentence, つまらぬ物 is the object that is affected by the action of the following verb.
And the verb here is 斬って which is the te-form of the verb 斬る meaning “to cut”. So つまらぬ物を斬る means “to cut a worthless object”. If you learned the kanji for “cutting” you might know this kanji (切る) which is commonly used. For example, リンゴを切る meaning “to cut an apple”. Whereas this kanji (斬る) is used when cutting something or someone by a sword. For example, 刀で人を斬る meaning “to cut a person by a sword”.
しまった is the past tense of しまう and the te-form of the verb followed by しまう means “to do something unintentionally”. It implies cutting a worthless object is not what Goemon wants to do and it is a regrettable thing for him.