If you keep going left, eventually you get past “liberal” and move on to Democratic Socialism, Socialism, Communism, Marxism, and so on…
The PLO is a kinda-sorta “terrorist” group these days, but is decidedly liberal when it comes to economics and social policy. For that matter, so are Hamas and Hezbollah, for the most part, especially if you discount the whole “crushing the Pirate State of Israel” thing, which is decidedly undemocratic.
“Spiking a tree” could mean driving a spike into it so that a logger could hit it with his chainsaw, a potentially fatal event. That would be terrorism, and there are certainly eco terrorists. Are they left wing because they are fighting against the big bad logging industry on behalf of the people who want to enjoy the beauty of a tree? Power to the people? Or are they just terrorists, trying to influence some aspect of their world in a very potent way? I think the latter. Not left wing or right wing. I think those labels don’t fit.
To expand on Really Not All That Bright’s point, you can think of politics as a sort of doughnut arrangement. If you start at the 'pragmatic middle-of-the-road" part of the doughnut and head either left or right, you encounter progressively more extreme views until you get to “rabidly narrow-minded violently oppressive”.
Those groups that are genuinely terroristic tend to blur together in the practical terms of their programme (do whatever we want or we’ll kill your family), irrespective of what brand of slogan they are spouting. Rather like the remarkable similarities between Hitler, Franco, Mussolini, Stalin, Mao etc.
At the extremes, I don’t think there’s a lot of point trying to distinguish between left and right wing - they’re all authoritarians of some kind.
Wikipedia describes the Palestinian Fatah Party as a centre left political group. The Black September movement that killed Israeli sports people in Munich were a splinter group from Fatah and could therefore probably be classed as a left wing terrorist group.