Use Google Chrome

• Go to page My network » Connections
• Select checkboxes for people to delete
• Open Console (or press F12)
• Run code:

JSON.stringify($('#list-panel input:checked').parents('li').map(function(){ return this.id; }).toArray());

• Copy generated code ( ["xxxxxxx","yyyyyyyyy","zzzzzzzz"] )
• Go to page Remove Connections
• In console paste generated code:

var ids = ["xxxxxxx","yyyyyyyyy","zzzzzzzz"];

• Run code:

$('#pickside input').each(function(){ ($.inArray(this.value, ids) !== -1) && $(this).trigger('click'); });

• Click button Remove connections