The voltage switched is completely unrelated to the switch controller, whether an Arduino or other device. The switchable voltage and the control voltage are characteristics of the relay or other switching device.
There is no reason why a 700 V rated relay should not exist, but, a quick look at Digikey's (a large electronic component reseller) catalog shows that they have no 700V or above rated relays in either mechanical or solid state versions.
While you could investigate other suppliers, this is a very good indication that what you are trying to do is "not a good idea". The problem is that you have told us HOW you wish to solve a problem . but not what the actual problem is.
"Tell us what you want and we'll tell you what you need".
What are you trying to achieve?
What is driven by the output voltage?
What current? What load characteristics.
It is likely that a "solid state" solution will meet your need - once we know what it is.
Digikey sells MOSFETs rated at 1000V and low current for under $1 and devices rated at 2500V and several amps for under $10. Whether any of these meet your need depends on what the need is.
This is a non trivial application and circuit complexity depends on whether you require simple on/off control or more complex waveforms.
I'd expect that the electroporation community would have addressed the requirement
for lowish cost semi-DIY power sources. Digikey have a number of high voltage IGBT devices suited to switching the voltages involved. Circuit design is liable to neither be rocket science nor trivial.
An example IGBT is the IXYS IXBH2N250 pricing and datasheet.
Rated at 2500V, 2A it seems a reasonably likely basis for a switch.
There are a reasonable number of others.
This thesis appears to be highly relevant
Design of a MOSFET-Based Pulsed Power Supply for Electroporation by Jason R. Grenier -- thesis University of Waterloo Master of Applied Science Electrical and Computer Engineering
The 2SK3748 MOSFETS are obsolete but still available from ebay and amazon suppliers.
2Sk3748 on ebay and Amazon.
I include the following two circuits from the thesis to show how notionally simple such a circuit may be. Neither circuit shows any means of output voltage monitoring or waveform control. If a relay would have been adequate then a circuit of this degree of complexity may suffice. Other MOSFETs that suit this circuit are available.
This paywalled paper sounds ideal. - They claim a $60 cost DIY device.
Their voltage is limited to 300 Volt maximum but this should be able to be easily extended.
Design and evaluation of an affordable and programmable mobile device, capable of delivering constant current and high voltage electric pulses of different waveforms for biomedical and clinical applications