First of all don't ever wash the cutting board in a dishwasher. If it was originally made with the old fashioned hide glue, hide glue breaks down with both heat and water but most glues weaken with heat.
To do it the easy way I would just use Titebond ll or lll on the joint that failed and clamp it up tight. Be prepared to fix it again in the future on some of the other joints but it's easier to reglue individual joints as they fail than try to glue up the whole board at once.
Then sand or scrape the surface smooth, disinfect with bleach, then treat with a food grade mineral oil/bees wax mixture. Don't use olive oil or other vegetable oils as they will turn rancid over time