I've got a couple of solutions for you; choose whichever sounds more manageable for your landscape project. First, you could rake off the mulch you applied, lay 4-6 sheets of newspaper over all of the grass, and spread the mulch over it all. The newspaper layer will smother the grass and eventually break down naturally.
The other option is a chemical one; spot-spray the grass with a herbicide like Roundup. You'll have to shield your plantings carefully from drift, because the herbicide can kill all plants. You might use a cardboard shield or -- if the plants are small enough -- overturned buckets to shelter them while you spray.