Please enlighten me about whether it says in Qur'an that if a person disrespects the Qur'an he should be killed, if the person is a Muslim. Does it matter if he is Muslim or non-Muslim? Some says that it means the Muslim person who disrespects the Word of Allah (swt) because he knows the real truth and denias it.

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
No doubt, that Qur'an is the "Speech of Allah" which was revealed to Muhammad (Blessing and peace upon him) through Gabriel (Alaihisslam). So, whoever defames it, contests it, or attributes it to someone other than Allah, he has contested one of the Attributes of Allah and that person is then a Kafir.
Allah Says (interpretation of meaning): {And truly, this (the Qur'ân) is a revelation from the Lord of the 'Alamîn (mankind, jinns and all that exists), Which the trustworthy Rûh [Jibrael (Gabriel)] has brought down; Upon your heart (O Muhammad SAW) that you may be (one) of the warners, In the plain Arabic language. } [26: 192-195]. Allah also Says: {Hâ­Mîm. [These letters are one of the miracles of the Qur'ân, and none but Allâh (Alone) knows their meanings.] A revelation from Allâh, the Most Beneficent, the Most Merciful. A Book whereof the Verses are explained in detail; A Qur'ân in Arabic for people who know. }[41: 1-3].
Allah The Almighty has threatened whoever says that the Qur'an is the speech of human beings with the Hell Fire. Allah Says (interpretation of meaning): {Then he turned back and was proud; Then he said: "This is nothing but magic from that of old; "This is nothing but the word of a human being!" I will cast him into Hell-fire.}[74: 23-26]. Allah states that whoever hates any of what Allah has revealed all his good deeds become fruitless. Allah Says (interpretation of meaning): {That is because they hate that which Allâh has sent down (this Qur'ân and Islâmic laws, etc.), so He has made their deeds fruitless. }[47: 9].
This is sound evidence that a rejection of any of what Allah has revealed is synonymous to apostasy from Islam.
All the Muslim scholars are agreed that contesting, deriding, or minimizing the Qur'an is Kufr, taking the person out of the Muslim community. The same rule applies to all kinds of deformation against the Qur'an or any denial of any part of it. So, if the Muslim does any of the above mentioned things he apostatizes. The verdict in his case is to be ordered to repent; if he refuses, he should be killed. The evidence for this verdict is in the Qur'an, the Sunnah and the Muslim consensus. In the Qur'an, Allah Says (interpretation of meaning): {And whatsoever the Messenger (Muhammad SAW) gives you, take it, and whatsoever he forbids you, abstain (from it). And fear Allâh; verily, Allâh is Severe in punishment. }[59: 7]. Allah also says: { And let those who oppose the Messenger's (Muhammad SAW) commandment (i.e. his Sunnah, legal ways, orders, acts of worship, statements, etc.) (among the sects) beware, lest some Fitnah (disbelief, trials, afflictions, earthquakes, killing, overpowered by a tyrant, etc.) befall them or a painful torment be inflicted on them. }[24: 63]. The Prophet also ordered to be killed whoever gives up Islam. Al Bukhari reported from a Hadeeth narrated by Ibn Abbas that the Prophet said: "Whoever changes his religion (Islam) kill him". All the Muslims from the companions of the Prophet till now are agreed on this verdict except some extremists whose opinions have no weight.
On the other hand if a Harbi the Kafir who is in the state of war with Muslims, disrespects the Qur'an, he has added more Kufr to his Kufr. The Harbi Kafir is called to do one of three things: become Muslim, give the Jizyah or fight.
As for the Kafir who is paying the Jizyah or the one who was given a peace covenant that links him to Muslims, if one of these disrespects the Qur'an, there is a disagreement among scholars over the verdict concerning such a person. Some scholars believe that he breaks by this act the peace covenant that was given to him and then his blood becomes lawful and should be killed. Other scholars have a different opinion clarified in Ibn Al Qayim's book "The verdicts of the Zimmi" which could be read for more details on this subject.

Allah knows best.