SOURCE

var Main = {
    methods: {
        getCheckedNodes() {
            console.log(this.$refs.tree.getCheckedNodes());
        },
        getCheckedKeys() {
            console.log(this.$refs.tree.getCheckedKeys());
        },
        setCheckedNodes() {
            this.$refs.tree.setCheckedNodes([{
                id: 5,
                label: '二级 2-1'
            }, {
                id: 9,
                label: '三级 1-1-1'
            }]);
        },
        setCheckedKeys() {
            this.$refs.tree.setCheckedKeys([3]);
        },
        resetChecked() {
            this.$refs.tree.setCheckedKeys([]);
        }
    },

    data() {
        return {
            data: [{
                id: 1,
                label: '一级 1',
                children: [{
                    id: 4,
                    label: '二级 1-1',
                    children: [{
                        id: 9,
                        label: '三级 1-1-1'
                    }, {
                        id: 10,
                        label: '三级 1-1-2'
                    }]
                }]
            }, {
                id: 2,
                label: '一级 2',
                children: [{
                    id: 5,
                    label: '二级 2-1'
                }, {
                    id: 6,
                    label: '二级 2-2'
                }]
            }, {
                id: 3,
                label: '一级 3',
                children: [{
                    id: 7,
                    label: '二级 3-1'
                }, {
                    id: 8,
                    label: '二级 3-2'
                }]
            }],
            defaultProps: {
                children: 'children',
                label: 'label'
            }
        };
    }
};
var Ctor = Vue.extend(Main)
new Ctor().$mount('#app')

<script src="//unpkg.com/vue/dist/vue.js">
</script>
<script src="//unpkg.com/element-ui@2.13.0/lib/index.js">
</script>
<div id="app">
	<el-tree :data="data" show-checkbox default-expand-all node-key="id" ref="tree" highlight-current :props="defaultProps">
	</el-tree>

	<div class="buttons">
		<el-button @click="getCheckedNodes">通过 node 获取</el-button>
		<el-button @click="getCheckedKeys">通过 key 获取</el-button>
		<el-button @click="setCheckedNodes">通过 node 设置</el-button>
		<el-button @click="setCheckedKeys">通过 key 设置</el-button>
		<el-button @click="resetChecked">清空</el-button>
	</div>
</div>

@import url("//unpkg.com/element-ui@2.13.0/lib/theme-chalk/index.css");