In addition to the Shia answer by user #4730... The linked page, in Persian, says only shortly and refers to another page in Arabic, http://lib.eshia.ir/11025/19/39/%D8%A7%D9%84%D9%86%D8%AE%D9%84 , and I see there 2 hadiths, Google's translation of them:
 1 - Muhammad bin Yaqoub, on the authority of Ali bin Ibrahim,
on the authority of his father, on the authority of Ibn Abi Omair, on
the authority of Husayn bin Bishr, on the authority of Ibn
Mudarib, on the authority of Abu Abdullah, peace be upon him, who
said: Do not cut fruits, and God will inflict torture upon you as a
 2- On the authority of Muhammad bin Yahya, on the authority of
Ahmad bin Muhammad, on the authority of Ahmad bin Muhammad bin Abi
Nasr, he said: I asked Abu al-Hasan, peace be upon him, about cutting
Sidr? He said: A man from your companions asked me about him? So I
wrote to him: Abu al-Hasan, may peace be upon him, cut Sidr and
planted grapes in his place.
I have found also a Hanafi answer in Russian: https://askimam.ru/fatwa/pokhorony/mozhno-li-sazhat-na-mogilakh-rasteniya/ . there is a quote from "Radd al Muhtar", and they say it is makruh.
Google's translation of the quote from Russian:
It is condemned to remove fresh vegetation and grass, as well as
non-dried plants from the cemetery, because, while they are green,
they glorify Allah, bringing relief to the deceased and leading to the
sending of God's mercy. (Ibn Abidin. Rudd-ul-Mukhtar. - Volume 2, p.
Google's translation of the Arabic quote:
He also hates cutting wet plants and hashish from the cemetery without
land, because as long as it is wet, God Almighty praises - so the dead
will be deemed dead and will be revealed with mercy.
I have found another 3 opinions in Russian: https://www.umma-42.ru/news-65165.html , I bring that opinions shortly:
- Qatar Fatwa Center: do not touch them, but do only what is needed.
- Sheikh Khalid bin Suud al Buleikhid, member of Science fund of KSA: it is allowed.
- Suleiman al Majid, member of Consultative palace of KSA: it is allowed.
And I want to quote Quran about trees. I quote Umm Muhammad (Sahih International) translation of Quran:
18.7 Indeed, We have made that which is on the earth adornment for it that We may test them [as to] which of them is best in deed.
22.18 Do you not see that to Allah prostrates whoever is in the heavens and whoever is on the earth and the sun, the moon, the stars,
the mountains, the trees, the moving creatures and many of the people?
But upon many the punishment has been justified. And he whom Allah
humiliates - for him there is no bestower of honor. Indeed, Allah does
what He wills.
55.6 And the stars and trees prostrate.
I think, trees on graves are almost same as trees on other places, and people should not harm trees and other living creatures without some strong need. I think cutting tree because it is old and going to fall and break tomb stones, or goig to fall on pedestrians or cars, may be valid reason, and just cutting old tree even if it is healthy yet, in order to use that tree material, can be valid reason, because if people do not cut it, it dies anyway and falls or dries, but, you should take in account that if it rots on its place, falling or staying, it also is not useless, because it gives material to many other living creatures.
Plants on human graves are dangerous to eat from them for humans, because they may have prions. Also prions of cows infected humans.