@tgbv Regardless if Cron is calling every minute, you can configure Laravel's Task Scheduler to execute your tasks whenever, or however frequently you desire. If there is nothing scheduled, Task Scheduler will just close and wait for the next call from Cron.
So, if you have a long running script, just make a task entry for something that runs every 2 minutes, or 5 minutes, or however long you think it needs.
For example:
$schedule->command('my-command')->everyFiveMinutes();
Cron can call Task Scheduler to run every minute, but that command will only execute once every five calls.
To answer your question, no it will not kill processes already running.
If the length of time to process is too much of a variable, then you could consider making some kind of process mutex, drop file, or lock-entry in a database to let future processes know that there is a job in progress and to die immediately.. so yes, handle it yourself in some way.