Strictly speaking, this quotation is not from the Diamond Sutra and is somewhat misleading when taken literally. Nonetheless, an explanation is appropriate.
The Diamond Sutra is about sunyata, the central teaching of Mahayana Buddhism. This teaching is about the twofold nature of consciousness itself. On the one hand, the Buddha spoke at great length about sankhara, those unconscious mental processes by which means we make sense of things and conceive of actions that make sense to us. It is by means of sankhara that it is possible for us to behave intelligently and compassionately. It is by correcting false or misleading sankhara that we make progress on the path to Enlightenment (Nirvana). It is by means of wholesome and true sankhara that we understand and care for our children. Such wisdom and compassion is in the realm of relative truth in the Mahayana teachings. The profound insights of the Theravadin Abhidhamma, including Nirvana itself, are all within the realm of relative truth. The Mahayana teachings do not negate the great value of the Buddhadharma. Instead, the Mahayana teachings make an additional and important distinction between sensation and perception. Sensation is present and very real without sankhara. Sankhara has the psychological function of making sense of sensation. Yet sankhara is arbitrary in the sense that it can cause true or false belief. We can perceive or misperceive a sensation. In contrast, the sensation is neither true nor false, it simply “is.”
On the other hand, there is the experience of sunyata. The experience of sunyata is a meditative state in which all sankhara are suppressed. Neither true nor false relative belief arise. As a result, the meditator gets to experience the universe as it really is without arbitrary conception (the products of sankhara). Then and only then, according to the Mahayana teachings, does a person get to experience absolute truth or sunyata. Only in this state does the meditator get to experience his true relationship with the universe. While in this state of awareness, all things are sunyata (empty). There is nothing to understand. There is nothing to be done. Yet everything is real.
In order to understand the Mahayana teachings, it is essential to not get confused as to what relative truth and absolute truth mean, especially when a person has not experienced sunyata. Let us return to the quotation provided. First of all, practice is based on relative truth. One does not “practice” sunyata. The term “no-things” is a somewhat misleading translation of the Sanskrit term “sunyata.” Strictly speaking, in order “to see, to perceive, to know, to understand, and to realize” anything, one must engage some form of sankhara. Finally, strictly speaking, it is misleading to say, “they ought not to conceive within their minds any arbitrary conceptions whatsoever,” because there is neither “ought” nor “ought not” in sunyata. In order to do something that we “ought” or “ought not” do, we must make a choice. And, in order to make a choice, we must engage some form of sankhara. Most important of all, while it is true that while in the state of sunyata, “all spiritual truths are no-things [sunyata],” all spiritual truths are true while not the meditative state of sunyata. Never, never, never use the great Mahayana teachings to claim that any relative truth is false. My suggestion is to get on with your practice and stop trying to speculate about what sunyata might mean.