I would make a turf stack, cover it and leave it for a year. When you use it you can always sieve it to remove any roots. Soil is expensive to buy so it is worth a bit of effort to reuse what you have.
You can put it in old compost bags - ensure you exclude the light - then leave them in an out-of-the-way corner and forget about them for about a year. Or if the volume is large, cover a pile with black plastic and leave for a good length of time.
You will then have some weed-free soil to use in the garden. Never throw away soil, if you can help it.
Try not to put it in the compost heap or any roots of perennial weeds will shoot next year and seeds will germinate.
The processes of decay will kill the living grass and weeds, eventually. The weed seeds will however remain in the soil, but lie dormant. As soon as you use the 'compost', and expose the seeds to the light, they will know it's time to wake up.
I don't know how long weed seeds remain viable. It probably depends on the species but can be several years.
In practise that isn't a problem. You'll just need to be prepared to some weeding.
But decent soil is a valuable resource, so make sure you reuse it yourself.