It depends if you have any perennial weeds like dandelions, clover,buttercup in the turf. If you chop these up with a rotivator every little bit will sprout into a new plant!

Volunteer is right, but digging a new garden is a lot of hard work. Personally I like to make a quick start by using a heavy mulch over the previous turf.
If your soil isn't a very hard pan into which you can hardly push a fork or a spade, this does work and makes for less work.
First, mow down the weeds and grass as low as possible.
Second, put down overlapping layers of newspaper, three or four pages thick.
Third, cover the layer with garden compost, well rotted manure, or mushroom compost. (This is the difficult bit if you have a large area).
Fourth, plant whatever you want to grow that year through the mulch and into the soil beneath, after a few weeks or so allowing the grass and weeds to die off under the impenetrable mulch.
In the first year I'd recommend you grow only annuals, whether vegetables or flowers, but if you pull out any weeds and grass that start to come through, by the end of the season you will have a good soil which will be much easier to work.
Deep mulch enthusiasts just keep piling on the mulch materials each year to build up the soil.
This works really well, even on heavy clay soil, for vegetables. I've much less experience in using this successfully with shrubs and flowers, but there's no reason you couldn't try this approach.