How can I process Vue.js props before actually using them?

I would say that computed properties are good for that:

Let's imagine this data:

let raw = [
    {
        id: 1,
        link: '/some-link',
        name: 'some-name'
    },
    {
        id: 2,
        link: '/other-link',
        name: 'other-name'
    }
]

And that component that takes this data in property:

<template>
    <div>
        <ul>
            <li v-for="item in formated"><a :href="item.href">{{ item.libel }}</a></li>
        </ul>
    </div>
</template>

<script>
    export default {
        props: ['raw'],
        computed: {
            formated () {
                let menu = []
                for(let i  0; i < this.raw.length; i++) {
                    menu.push({
                        libel: this.raw[i].name,
                        href: this.raw[i].link
                    })
                }
                return menu
            }
        }
    }
</script>

As you can see, the formated method is a computed property that will update each time your raw property change.