[Vuejs]-V-html attribute doesn't update

Looks like this is your problem: you’re referring to this inside a (non-arrow) function in your then. Do you mean to have the function keyword in there?

   methods: {
        update(url) {
            axios.post(url, {
                _method: 'patch',
                body: this.body
            }).then(response => function () {
                this.body = response.body;
                this.parsed_body = response.parsed_body;
            });

            this.editing = false;
        },