I'm a clonidine veteran, much like a lot of the other opiate fiends on BL. I've been prescribed it off an on for withdrawal management and mild hypertension. Are the two mutually exclusive? Who knows. Anyway, OP, like others have said, the best way to go about this is to taper. Can I inquire as to the current dose that you're withdrawing from?
I've now been taking clonidine for 2 years as it helps with the jitters from my anxiety and my inability to sleep. Sometimes I pop an extra pill at bed time if I can't get to sleep, or I'll take an extra one when I'm hungover to alleviate some of the body load of the experience. I've run out early before several times. Bear in mind that I was taking a total of 0.6mg per day; a moderate dose. Everyone's experience varies of course, but I always found the "withdrawal" to be relatively mild. You can expect a marked rise in blood pressure, tightness in chest, heart palpitations (feels like your chest is pounding like a drum during even limited exertion) and maybe some excess anxiety.
If you are out of pills, grit your teeth and bear it provided you're not taking them for serious hypertension. If you have pills, do a quick taper. It shouldn't be an incredibly long process. Reduce your dose by quarters. You can break pills apart yourself and guesstimate the dose, but for this process, I would highly recommend a dedicated pill cutter. They're cheap and work great.