You could use a combination of an Array and an v-for statement

Basically:

//The UI
    <ul>
        <li v-for="(item, key) in array" v-bind:key="key">
            //Here you can use now every item in the Array like this for example
            <span>{{ item.name }}</span>
        </li>
    </ul>

//The code
export default {
    data() {
        return { array: [] };
    },
    methods: {
        apiDataFunction() {
            axios
                .post('xxx') //Or whatever you have
                .then((res) => {
                    this.array.push(res.data);
                });
        }
    }
};

If you could give some more information I could help more. For example, how the data looks that you retrieve with axios etc.

I didn't test this code personally so it may be, that you would need to pack this array into an computed statement