You can use a leader to start so that your fabric doesn't get sucked in or you can use a piece of stabilizer either tear away or water, put it under the fabric with a little sticking out to hold onto and it'll prevent those points from going into the hole. If you have a single hole needle plate this would also be the time to use it.
The biggest thing about cutting with the Accuquilt, you have to pay attention to the grain or the size won't be right. Ask me how I know this.