"stamp down" is a correct and usable phrase in written English.
It is used as a phrase meaning to forcefully press down with your foot (for example on a pedal or gas), or to express a strong disapproving opinion (for example towards a behaviour). Example: After hearing his boss' angry rebuke, Tim stamped down to his chair.
Without Lincoln's help, they would be "Stamp down or trodden under feet by our Superintendent".
To have Boris' jackboot stamp down on legitimate debate is ludicrous".
Corbyn used the speech to stamp down his authority by offering no apology for his pro-immigration stance.
But along with supporting hard-pressed public services, the fund will be used to help councils stamp down on wrongly claimed housing benefit and rough sleeping.
I've perfected the "safe walk" where I stamp down with each step, as if mashing grapes, while holding my arms out like a penguin.
We must continue to stamp down on problems like "dishonoured" daughter punishment, female circumcision, and "exorcism" abuse, and encourage everyone to learn English.
Team members often have to spend hours packing the slopes by stamping down the snow.
When the Kazantip organisers saw the footage they stamped down on such behaviour and the 'sexy displays' were suspended when we were there.
A decade on and Mr Lukashenko's security services – which still use the KGB moniker – are back in action, stamping down on pro-democracy activists and arresting hundreds.
Kerr was said to have performed a "long jump" motion as he brought both feet stamping down on his victim in the "vicious attack" on August 31 2014.
The ADB argues that governments could do much to change this: from investing more in education and infrastructure, to stamping down on corruption and improving the regulatory environment.
