It's a typo and should be a Constitution saving throw
As confirmed by the official errata that @Eddymage found, this ability should be using a Constitution saving throw.
This also makes sense when looking at the context: The 2014 version of the Carrion Crawler called for a Constitution saving throw:
Tentacles. Melee Weapon Attack: +8 to hit, reach 10 ft., one creature. Hit: 4 (1d4 + 2) poison damage, and the target must succeed on a DC 13 Constitution saving throw [...]
This used to be an ability that required the Carrion Crawler to make an attack roll. Upon a hit, the resulting Constitution saving throw does not have the issue that the Dexterity saving throw has, because being paralyzed did and does not mean that you automatically fail Constitution saving throws.
In the new version, the ability does not require an attack roll any more; instead, it was switched directly to an effect that requires a saving throw. Dexterity is the typical saving throw that is used to avoid being hit by attacks or spells to begin with, so it makes sense that for avoiding the initial hit, this would be switched for a Dexterity saving throw. But that then does not work any more when you have to repeat the saving throws.
An alternative solution could be to make the first saving throw a Dexterity one, to avoid being hit, and then use Constitution for the following saving throws, to shake off the Paralyzed condition. However, this does not work with the way the ability is templated. Narratively, you also can justify directly using Constitution, as you are not only trying to avoid being hit, you're also trying to avoid being affected by the tentacles' poisonous mucus when hit. So maybe there is no way to avoid being hit, but you still can resist the effect.
