Mark 1:1-3 quotes two other passages from the Bible, so they must be taken into account to get the context of these verses in Mark. The first quote found in verse 2 is of Malachi 3:1 (quote in bold):
“Look! I am sending my messenger, and he will clear up a way before me. And suddenly the true Lord, whom you are seeking, will come to his temple; and the messenger of the covenant will come, in whom you take delight. Look! He will certainly come,” says Jehovah of armies.
This verse mentions three entities: "my messenger", "the true Lord", and "the messenger of the covenant". The first messenger must be John the Baptist, and Jehovah God is the "true Lord" whose "way" is being cleared up. Jehovah's Witnesses believe that Jesus accompanied Jehovah God as the "messenger of the [Abrahamic] covenant" to cleanse the temple and to first grant the opportunity of becoming Kingdom heirs to the Jews. —Insight, Vol. 2 pg. 385.
The second quote found in Mark 1:3 is from Isaiah 40:3:
A voice of one calling out in the wilderness:
“Clear up the way of Jehovah!
Make a straight highway through the desert for our God.
This prophecy speaks of the "way of Jehovah", which is a common expression in the Bible that refers to a right and just way of living that is approved by God. This prophetic concept of a "highway" appears in several places: Isaiah 11:16; 35:8; 49:11; 57:14; 62:10; Jeremiah 31:21. It is clearly not a literal path which John the Baptist was calling to clear, but a figurative one. He was calling people to pure worship, preparing their hearts to obey Jesus' commandments, which come from Jehovah. (John 7:16-18) Jesus himself is known as "The Way". —Acts 9:1, 2; 19:9; 22:4.
Therefore, having a thorough understanding of the prophecies at play in Mark 1:1-3, we can show that John the Baptist's call to "clear up the way of Jehovah" is understood to refer to Jesus as Jehovah God's messenger and representative, and as the role model (or "Way") which God's people use to come to a close relationship with Jehovah God.