<el-table 
    :data="tableData"
    ref="selectTable"
    @row-click="rowClick"
    @selection-change="handleSelection"
>
</el-table>

rowClick(val) {
    this.$refs.selectTable.toggleRowSelection(val)
}
handleSelection(val) {
    if(val.length > 1) {
        this.$refs.selectTable.clearSelection()
        this.$refs.selectTable.toggleRowSelection(val.pop())
    }
}

thead {
    .el-checkbox {
        display:none;
    }
}