Is there a DIY way to kill grass?

I wanted to plant a medium sized flower bed around my mailbox. I had been told by a friend that, as long as I added at least 3 layers of mulch that there was no need in removing the grass first. He was way wrong! I put in a good 4-5 inches of mulch and 2 rainy days later, the grass is already coming up through the mulch. I'm hesitant to use a chemical grass killer because I worry it will damage the new plants (knockout roses backed by crape myrtles). Any suggestions or advice would be greatly appreciated. I'm hoping that I will not have remove the mulch and put down a weed barrier.
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