My mortgage rate is many times higher than the interest rate on any of my savings accounts. I can try to get better accounts like an Money Market or a Certificate but I'd have to drop like 100k, which I don't have, just to get a rate comparable to my mortgage.
My mortgage is young so its currently over twice higher than my other assets. $1k in a certificate gets me $50 in a year. $1k lump to my mortgage saves me $2k in future payments. $1k extra annually saves me $15k. If I kept reinvesting that certificate I'd earn about $4K over the same timespan.
As I see it, I should be dumping much money into my mortgage as I can afford right now. Maybe when the account gets smaller than my other assets that'll change. But for now the only thing stopping me is having some actual liquid savings.
Advices here have rightfully told you to pay off higher interest debts (ie your mortgage) before saving in lower interest saving accounts.
Only addendum I have is that, unlike savings accounts, money you pay into your mortgage is money you can't pull back out. Don't forget to keep at least a few months of emergency funds, and be aware of any upcoming large costs, before dumping all extra cash in the mortgage.
Paying off 6k of mortgage, then one month later having to take out a high interest loan for 6k for necessities, is not ideal.