A mower and/or a weed whacker would be your best options. A mower will work more quickly if it is a large, flat, open area, but if you need to work around a lot of complex angles and surfaces a weed whacker is the way to go.
Also, don't worry about composting that material. Bermuda-buttercup (
Oxalis pes-caprae) does spread by bulbils in the soil, but leaves, stems and flowers will not act as propagules, and it does not even produce seeds outside its native range in South Africa.
By the way, do you have any photos of the plant that you thought was kudzu?
https://www.gardening-forums.com/threads/how-to-get-rid-of-kudzu.16473/