Boss won't waive my 2-month notice, new job can't wait. Options?

Yes you can buy out. Under the Employment Act, either party can terminate the contract by paying salary in lieu of notice for the unspent portion. So you can legally leave early by paying your boss one month's salary (the difference between 2 months and the 4 weeks you'd serve). He cannot force you to physically stay if you compensate, that would be forced labour. Steps: 1) Send a written notice stating your intended last day and offer payment in lieu for the shortfall, quote the compensation-in-lieu clause. 2) Ask your new employer if they'll reimburse the buyout, many will for a candidate they want, I've had one cover it fully. 3) Keep everything in email. Don't just walk out without the in-lieu payment or you could be in breach. But done properly, notice buyout is your right, not his mercy. Spite is not a legal basis to trap you.

Ask your new employer to negotiate the start date first, it's the cleanest option. Many companies understand a 2-month notice and will push their start date. I've delayed a start by 3 weeks with zero issue because they wanted me. Only resort to buyout if they truly can't wait. Buyout is real and legal but costs you a month's pay, so exhaust the free option first.

Also use your annual leave to offset. In SG you can often apply to clear accrued leave during the notice period so your effective last physical day is earlier, though the boss can reject leave. But many contracts let you offset leave against notice. Check yours. I cleared 12 days leave and shaved my notice down considerably.

If your boss is being spiteful, keep it strictly professional and paper-trailed, because a bitter boss might try to withhold your final pay or give a bad reference. Do everything by email, hand over cleanly, and if he withholds salary you can file with MOM/TADM. Don't give him ammunition. Leave classy and let his pettiness be his problem.