Jim Currie said that he had 'pushed the cause of retaining Council control over joint ventures as far as [he could] with the Cabinet' and that the financial risks involved with the 'rush' into strategic partnerships were 'unacceptable'.
Outsourcing of the council's services could go to either BT or CSC if the plans go ahead in a deal that is worth up to £300 million a year.
In September last year councillors voted to postpone the signing of contracts, but cabinet members forged ahead regardless.
However, a successful petition has resulted in plans for a full-council debate, which will take place on 23 October.
Alec Robertson also faces a vote of no confidence on 16 October.
Liberal Democrat Cornwall Councillor, Jeremy Rowe, wrote in his online blog that "the importance of the no confidence motion on the 16th grows greater by the day."
He added: "The personality clashes in this saga point to a leadership which has lost control and is completely out of touch. When your own hand-picked Deputy smells a rat you know something's up."
The tone of Currie's resignation email implies that, despite the plans for a full-council debate, Robertson is unwilling to relinquish the privatisation plans.
He said: "I welcome your somewhat ambiguous offer to respect full council decisions on the 23 October, but I know you will never let go.
"I could not leave local government with billions of pounds of Cornish taxpayers' money at risk and on my conscience."
Currie finished the email by saying: "Alec, this matter has never been personal."
Robertson has said that under the proposals, either BT or CSC would be legally required to deliver at least £5 million of savings over the next two years and to create a minimum of 500 net new jobs in Cornwall.
Robertson said in a statement: "The reality is that both companies are offering to deliver even greater savings and create more jobs than we set out in the original prospectus which can only be good news for both the Council and people in Cornwall.
"I am hopeful that members will support the strategic partnership once they have access to all the facts. However, if I a majority of the council decide to vote against the proposal, then it will not go ahead."