Are you trying to put Blade inside your Vue component, like inside the Browserify .vue file? I don't think that is possible. Generally you don't use Javascript libraries a lot where SEO is crucial. I don't know the exact situation, but can't you attach the vue component to every item in the list? You can make directives so you do something like
@foreach ($items as $item)
<li vue-this>$item->text</li>
@endforeach
Then you can add behaviour when people do whatever with that list item. I don't think that intervenes much with SEO. But again, I would simply step down Vue on the SEO crucial pages and rely more on Vanilla.