You have no entitlement to a severance payment other than your contractual notice. If your employer exceeds this, then I believe it is not taxable if it is an ex-gratia payment, although I tried to get some advice on this point and failed miserably. Notice is pay so is taxed as such.
If you work for an MNC and can get them to pay you the ex-gratia bit offshore then as I understand the situation, it would not be related to employment in Singapore (because it is ex-gratia) and so provided you dont remit it here, it wouldnt be taxed here. Shouldnt be taxed in jurisdiction it is paid either as not effectively connected with employment there. Eg, I work for an English MNC, and am made redundant. Paid 1 months notice in Singapore, and GBP25,000 in UK ex-gratia. GBP25K would not taxed. Not sure what the position would be if the 25K had exceeded 30K tax free threshold in the UK but think it would still be non-taxable, or at least would be reduced by personal allowances, service averaging provisions etc (eg if worked in Singapore for half the time and UK for half the time only half the excess would be taxed)
I Think it really depends how your employer will report it. if they report it to IRAS as income, you will be expected to pay tax on it. if not, you wont.
Sorry to be so vague but hope it is a bit helpful.