The axe is a common heraldic charge, just as the cross is a common Christian symbol. An Axe Cross is an attempt to portray a fighting weapon as a Christian symbol.
Where a hammer is generally a tool used in construction, an axe is generally used for destruction. And yet that destruction could be a preliminary stage in the construction of something. You can't make an omelette without breaking eggs.
The axe is prehistoric; it has been used since the Stone Age for chopping down mighty tress and for hacking up animal carcasses. A man with an axe is not to be argued with and it has long been a symbol of strength and authority. Mussolini adopted a symbol which included an axe, and the implement has been for a long time the only friend of an executioner.
But the axe is not always used for demolition work. It is still a piece of equipment for firemen would not do without. The fireman's axe may have saved as many lives as the battle axe has ended. Artists also use the axe to shape stone, wood or ice, to produce remarkable sculptures.
But in heraldry, the axe represents fighting and can be disguised as a cross to give a certain legitimacy to a warrior's profession.
On the right we see the tomb cover of Hugo de Pikeworthe (Hugh de Pickworth)1, c.1325, in Selby Abbey, North Yorkshire. He was a knight who fought for Edward II in Scotland early in the 14th century.
(Edward lost control of the north of England and suffered an unfortunate reputation of being somewhat an incompetent king; one of his few accomplishments being born the son of the better known of Edward and Eleanor and his less prestigious royal acknowledgement of a certain fish. See Sam's Sturgeon.)
His shield bears six pickaxes. 'Six' is not understood to have any particular religious or military significance, but matches the six martlets2 on a tomb on the opposite side of the nave, being the the coat-of-arms of Margery, Hugo's wife.
It should be noted that rather than being a chopping axe, the type is a pick-axe, and happens to be an appropriate symbol for the name 'Pickworth'.3
It is not known whether Hugo actually used an axe to fight the Scots and it is not known how many people died in the campaigns. We do not know the names of the fathers and sons who were killed on both sides of the border. Indeed, we are not too sure what they were fighting for, other than they were ordered to fight by their lords who were attempting to gain power and control of lands.
With both sides struggling to satisfy their greed, there was nothing Christian about the fighting. Even so, the cross was, and still is today, an icon to imply righteousness where none exists.