the text should be handled by the state

therefore you must only edit the state of the component so that your changes are shown

import React from 'react';
import RaisedButton from 'material-ui/RaisedButton';
import TextField from 'material-ui/TextField';


export default class CreateLinksave extends React.Component {
  constructor(props){
    super(props);
    // initial state
    this.state = this.getDefaultState();
  }

  getDefaultState = () => {
    return { text1: '', text2: '' };
  }

  clear = () => {
    // return the initial state
    this.setState(this.getDefaultState())
  }

 render() {
  return (
    <div className="container">
      <div>
          <TextField
            value={this.state.text1}
            onChange={(e)=>{this.setState({text1: e.target.value})}}
            floatingLabelText="Receipt Desc"
          />
      </div>
        <div>
          <TextField
            onChange={(e)=>{this.setState({text2: e.target.value})}}
            value={this.state.text2}
            floatingLabelText="Triggers Required"
          />
        </div>
        // use the clear function
        <RaisedButton label="Clear" onClick={this.clear}/>
    </div>
  );
 }
}

If anyone has the same issue with the functional components in React, then you have to handle the value of the Textfield component with a state. Doesn't matter whether you use Formik library or not. Simple control the value property of the text field using a state variable.

import React from 'react';
import TextField from '@material-ui/core/TextField';
import Button from '@material-ui/core/Button';

const sampleTextControl = () => {
  const [value, setValue] = useState(''); //Initial value should be empty
  const handleSubmit = (e)=> {
    alert('The value: ' + value);
    setValue('');                        //To reset the textfield value
    e.preventDefault();
  }
  
  return ( 
    <form onSubmit={handleSubmit}>
      <Textfield id="standard-basic" value={value} onChange={(e)=>setValue(e.target.value)}/> 
      <Button variant="contained" type="submit" value="Submit">
        Submit
      </Button>
    </form >
  )
}

<script src=""></script>
<script src=""></script>
<script src=""></script>

If you don't want to manage state for every text field then you should use refs:

import React from 'react';
import RaisedButton from 'material-ui/RaisedButton';
import TextField from 'material-ui/TextField';

export default class CreateLinksave extends React.Component {
    constructor(props) {
      super(props);
      this.receiptRef = React.createRef('');
      this.triggersRef = React.createRef('');
    }

    handleClick = () => {
       this.receiptRef.current.value = null;
       this.triggersRef.current.value = null;
    }

    render() {
        return (
            <div clssName="container">
                <div>
                    <TextField floatingLabelText="Receipt Desc" />
                </div>
                <div>
                    <TextField floatingLabelText="Triggers Required" />
                </div>
                <RaisedButton label="Clear" onClick={this.handleClick}/>
            </div>
        );
    }
};