Shahob I

<input type="file" accept="image/*" @change="handleChange($event)" id="file-input">
<button v-on:click.prevent="handleSend">Отправить</button>

new Vue({
    el: '#app',
    data: {
        name: 'John Doe',
        keywords: 'key',
        form: new FormData()
    },
    methods: {
        handleSend: function () {
            // upload image
            axios.put(
                '/upload',
                this.form, {
                    header: {
                        'Content-Type': 'image/png'
                    }
                }
            ).then(response => {
                console.log('image upload response > ', response);
            });

            // send form
            axios.post('/api/crud', {
                name: this.name,
                keywords: this.keywords,
                title: this.name
            }).then(response => {
                console.log(response);
            }).catch(error => {
                console.log(error.response);
            });

        },
        handleChange: function (event) {
            this.form.append('name', 'my-picture');
            this.form.append('file', event.target.files[0]);
        },
    }
});