This is a song with a finger pointing purpose, namely targeting the KKK, which it directly addresses in the 7th of 7 verses:

This song is just a reminder to remind your fellow man
That this kind of thing still lives today in that ghost-robed Ku Klux Klan

Dylan aims at a moment in a horrible chapter of American history, a time when the nation was becoming all too familiar with the atrocities of racism and corrupt courtrooms.  But the word was getting out, and the following years would result in the Civil Rights Act.  No legislation stops hatred outright and certainly not right away, but it could begin to invoke fear, which can only approximate Emmett Tills’ fear that Dylan makes it hard for us to face with lines like this:

Some men they dragged him to a barn and there they beat him up
They said they had a reason, but I can’t remember what
They tortured him and did some things too evil to repeat
There were screaming sounds inside the barn, there was laughing sounds
out on the street

They rhyming pattern when it is in a pattern goes like this:  aabb, but Dylan can’t keep to it, as if the subject matter is too severe to keep to any concordant sounds.  In fact, the opening verse has no terminal rhymes:

’Twas down in Mississippi not so long ago
When a young boy from Chicago town stepped through a Southern door
This boy’s dreadful tragedy I can still remember well
The color of his skin was black and his name was Emmett Till

The l’s that end well/Till have a timbre to them, but that’s not a rhyme. The rhyming is slow in coming, as if narrative matters more. what/up is close, but it’s a forced rhyme at best beginning the second verse:

Some men they dragged him to a barn and there they beat him up
They said they had a reason, but I can’t remember what

repeat/street enters as the first real rhyme at the end of the second verse, and then the aabb pattern emerges in verse 3:

Then they rolled his body down a gulf amidst a bloody red rain
And they threw him in the waters wide to cease his screaming pain
The reason that they killed him there, and I’m sure it ain’t no lie
Was just for the fun of killin’ him and to watch him slowly die

Bit it doesn’t last.  The name Till won’t rhyme with trial:

And then to stop the United States of yelling for a trial
Two brothers they confessed that they had killed poor Emmett Till
But on the jury there were men who helped the brothers commit this
awful crime
And so this trial was a mockery, but nobody seemed to mind

Refuses, too, even.  It’s as if the discordance is there because of the previous verse’s concordance–it’s accentuated–there will be no agreement in sound between that trial and the crime that killed Emmett Till.

Once the trial is “over” in the song, the pleasing to the ear rhyming pattern returns:

I saw the morning papers but I could not bear to see
The smiling brothers walkin’ down the courthouse stairs
For the jury found them innocent and the brothers they went free
While Emmett’s body floats the foam of a Jim Crow southern sea

And rhymes flow free the rest of the way, perhaps so the song can be sung, remembered, as all tragedies of such human indignity and cruelty must:

If you can’t speak out against this kind of thing, a crime that’s so unjust
Your eyes are filled with dead men’s dirt, your mind is filled with dust
Your arms and legs they must be in shackles and chains, and your blood
it must refuse to flow
For you let this human race fall down so God-awful low!

This song is just a reminder to remind your fellow man
That this kind of thing still lives today in that ghost-robed Ku Klux Klan
But if all of us folks that thinks alike, if we gave all we could give
We could make this great land of ours a greater place to live
A hopeful ending to a painful song.

Here’s Dylan performing it on the Radio Show with Cynthia Gooding March 11th 1962: