The hearing was due to take place on 28th May but has now been adjourned until 12th August.
The trees were felled late in 2018 in the outlying village of Penllergaer, near to a housing development being completed by Enzo's Homes of Llanelli.
The work drew local concern, prompting an online petition which drew nearly 5,000 signatures.
Following a five-month investigation by Swansea Council and Natural Reseources Wales, the council issued a court summons to Enzo's Homes, its director Fiorenzo Sauro and tree contractor Arwyn Morgan of AOM & Associates, also based in Llanelli.
Cabinet member for environment and infrastructure management Mark Thomas said: "This case is something we have taken very seriously and it has taken a lot of hard work to get to this stage. It has taken months of investigations and assessments of the site in question - which is in private ownership and not part of the development site at Penllergaer."
He added: "There has been a huge amount of interest in this incident by the public who feel the same way as we do when part of our natural environment is destroyed. I'm pleased we are taking appropriate action which will hopefully send a message out to others that destroying protected trees is something we will not tolerate - whether it's one tree, or in this case around 70."