The early scholars, known as the ‘Church Fathers’, agree that the book of Matthew was first written in Hebrew:
Papias (ca. 130 after Yeshua): “Matthew composed his work in the Hebrew dialect, and each translated as best they could.”
Irenaeus (ca.170 after Yeshua): “Matthew also issued a written Gospel among the Hebrews in their own dialect.”
Origen (ca. 200 after Yeshua): “The first [Gospel] is written according to Matthew, the same that was once a tax collector, but afterwards an emissary of Yeshua the Messiah, who having published it for his believers, wrote it in Hebrew.”

Matthew 8:21-22 [The Scriptures 1998 - TS]
21 And another of His taught ones said to Him, “Master, first let me go and bury my father.” 
22 But יהושע{Yehoshua} said to him, “Follow Me, and leave the dead to bury their own dead.”
[Words of Yeshua in purple]

But, who are these dead that bury their dead? 
There are some who believe that the dead in this text are the ones who did not follow Yeshua wherever he went, as opposed to his followers. In other words, those who do not follow Yeshua are dead. And so the message of Yeshua, they say, is that his followers are spiritually alive and those who do not follow him are spiritually dead.
The problem with this interpretation is that it is unreasonable for Yeshua to expect that everyone follow him wherever he went. The old, the sick, the mothers taking care of small children could not be expected to follow Yeshua. Are these people dead?
It makes no sense to identify these people as ‘dead’ when they have a logical reason for not following Yeshua wherever he went.
Perhaps it was said correctly but read incorrectly.
Certainly, these verses seem enigmatic as they appear in the Greek manuscripts. To understand them correctly we would need more information and more context. Some logical questions would be:
Did the father die recently? Was he sick and not yet dead? Was the elderly and his son wanted to take care of him until the time of his death?
Another possibility would be the ‘second burial’:
During the first century, Yeshua’s time, it was customary to bury a dead person twice. The first time would be at the person’s death and the second time would be a year later when the bones were put in a stone box for bones called an ossuary.

All these questions disappear if we read the text in a different way.
The Hebrew word המתים ׁׁׁ(hey, mem, tav, yud mem) without vowels, as it is written in the Hebrew Matthew, could be read as:
הַמֵּתִיםHa-Metim ׁ(the dead)  let the dead bury their dead  or
הַמְּתִים – Ha-M’tim (the men)  let the men bury their dead  or
הַמַּתִּים – Ha-Matim (the close relatives)  let the close relatives bury their dead

The third option is the most probable one because it makes the most sense. The text is no longer ambiguous if we read Ha-Matim and not Ha-Metim. It becomes clear when we read ‘let the close relatives bury their dead’ and not ‘let the dead bury their dead’.

Matthew 8:22
...follow me and let the close relatives bury their dead

When we read it this way, the enigma disappears. Yeshua’s answer is clear and logical. It resolves the problem in a practical way.

What Yeshua said in Hebrew was perfectly understood. But once his words were written, some of them became unclear and vague because the vowels were not recorded along with the consonants.
Main source: Avdiel Ben-Oved; translated by Nazarene Notes