You can create an opacity mask to achieve that.
I assume the background vector image to be cut is in a group. If not, then make sure you group it before continuing.
Type some black text over the image you want to cut out
With the Selection tool (V) select both the background group, and the text
Open the Appearance panel, and click on the Opacity
Click Make Mask
Deselect the Clip option.
I have also added a beige shape in the example below, so you can see that the blue background is actually cut out by the opacity mask.
The beauty of this method is that it's non destructive. The text inside the mask is still editable. You can enter the mask by clicking on the mask thumbnail in the opacity panel, edit the text, move it etc, and exit the mask by clicking back on the object thumbnail.