The company has admitted the cuts are being made for commercial reasons, having blamed a previous round of changes on a Covid-induced driver shortage.
The operator said last week the vast majority of the cuts would go ahead.
Some new services brought in to partially compensate for the changes will be beefed up with extra journeys, however.
But speaking at a full council meeting on Wednesday, Labour councillor for Wakefield West, Kevin Swift said: “The bus industry is in a state of crisis.
“Much like the NHS, it went into the Covid period in a very weak state and the impact of Covid has been to expose the deficiencies and shortcomings in the industry.”
Councillor Swift said Arriva were making the changes, “very nakedly for commercial purposes and it’s no longer clouded in the language of staff shortages and greater reliability".
He added: “Please Arriva, hold back, it’s premature.”
Coun Swift warned further cuts are likely to come and that efforts to bring West Yorkshire’s bus system under public control was “being made bureaucratically very difficult”.
The region’s mayor Tracy Brabin, who has started that process, has also blamed government-enforced timescales for the delay.
The leader of Wakefield’s Opposition Tory group, Nic Stansby, said: “I’ve noticed that Leeds gets what Leeds wants.
“If they want Smart Buses ,where people can ring up and pay £2 for a bus that stops 200 yards from their houses, then they get it.
“We’re very much the poor man in this relationship and you (Labour) have our full support to go and fight for us, because we’re not coming out of this as well as Leeds.”
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