My alternative is to put up a sign "Keep Out: Testing Lasers from
Space" which is a derivative of this idea and (IMO) would be
considered humor. I know there is a line, how and where is that "line"
defined?
This distinction captures the key point. If your sign stating "Active Mine Field" would, in the overall context, be understood as humor and not as a true statement of fact, it will be protected by the First Amendment.
If, however, someone is basically defrauded by a sign, because it appears to a reasonable person to be making a true statement of fact upon which a person reasonably relies to their detriment (or perhaps could reasonably rely to their detriment for criminal law purposes), then it is probably not protected.
For example, suppose that your "Active Minefield" sign causes the fire department, when responding to a wildfire next door to your property, to take the long way around your property or to call in the bomb squad at great expense. You could have civil liability as a result. Similarly, if the fire department refused to respond to a fire on your property due to such a sign, your insurance company might have a ground to deny your insurance claim for damages that a prompt fire department response could have prevented.
And @user6726 points out circumstances where there could be criminal liability, although there, as in the civil case, the First Amendment would require those criminal statutes to be employed in enough of a common sense fashion to only be invoked in cases where a reasonable person would believe the sign to be purporting to be a true statement of fact in the overall context of the situation, in order to withstand an "as applied" constitutional challenge to a facially valid statute.
So, a "space lasers" sign (at least as of 2022 when there are no such things) would probably not give rise to legal or civil liability, but an "Active Minefield" sign without something involved in the presentations to clearly indicate that it is a joke (or a fictional depiction for temporary theatrical purposes, for example) to a reasonable person, could result in civil or criminal liability.
Similarly, if the sign was very artistic and also had pictures of Bugs Bunny and Coyote chasing each other, and images of obviously fake "land mines", or if the sign were accompanied by a picture of cow turds everywhere that made clear that the "minefield" was a field full of excrement rather than high explosives, it wouldn't be actionable.
