In a resignation letter the Stafford MP told Mr Johnson she had lost confidence in his leadership and branded his administration a "debacle".
And she made it clear his handling of the scandal surrounding Mr Pincher was central to her decision.
It came after Nicola Richards became the first Black Country MP to speak out against the PM, with the West Bromwich East MP criticising his "poor judgment" as she resigned from her PPS role.
In her letter Ms Clarke, who was elected in 2019 and campaigned for Mr Johnson in his London mayoral campaigns, said: "I no longer have confidence in your leadership."
She added: "As one of the party's new female MPs and a member of the Women and Equalities Select Committee, I take allegations of sexual misconduct very seriously.
"To learn that you chose to elevate a colleague to a position of pastoral care for MPs, whilst in full knowledge of his own wrongdoing, shows a severe lack of judgment and care for your parliamentary party.
"I was shocked to see colleagues defending the government with assurances that turned out to be false.
"This is not the way that any reasonable government should act.
"It is our hard-working volunteers and local councillors who ultimately take the fury from the public and often end up paying the price for these failures of leadership.
"I think that we need to draw a line under the current debacle and get a grip on government on the public's behalf, as well as, most importantly, the country."
Ms Clarke backed Mr Johnson in last month's confidence vote. In May she welcomed him to Staffordshire as part of a 'Cabinet day' in the county.