Disculpar & perdonar mean 'to forgive', and they are in their infinitive form, as you wrote them, you conjugate them according to the person and time, to say sorry. They're interchangeable.
Dispensar in this sense, is the first time I my life I hear it. Thanks a lot to Naharror for teaching us something new. Still, I wouldn't recommend you to use it, many natives like me will hear it for the first time.
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According to the RAE:
Dispensar
(Del lat. dispensāre).
1. tr. Dar, conceder, otorgar, distribuir. Dispensar mercedes, elogios.
2. tr. Expender, despachar un medicamento.
3. tr. Eximir de una obligación, o de lo que se quiere considerar como tal. U. t. c. prnl.
4. tr. Absolver de falta leve ya cometida, o de lo que se quiere considerar como tal.
So using the logic, the form for 'sorry' could be the number 4. To absolve the person from a fault which is not so important, right? Hope it's so.
Best regards,
Alejo.