Truthfully, you can (and at a fixed cost – see MyScottishDivorce) but I must also say that divorce is usually preceded by a separation agreement.
That is the expensive part and the worst of it is that there is no fixed cost for that. Each of you will need a Solicitor.
What you need to agree in a separation agreement are issues about the children. With whom did they stay and when? What are the arrangements for contact?
There is also the vexed question of who pays what? There may be housing costs and, if you are fortunate, you need to divide up money and pensions.
The separation will cover other issues including inheritance rights and ensuring that there are no other claims.
I counsel you not to get divorced before signing an agreement! After divorce it is too late to claim…
However, once all that is done then what do you have to do about a divorce depends upon whether there are children under 16.
If there are not, it is easy-one of you fills in the form available from the court and it is over in a matter of less than a month. See MyScottishDivorce.
If there are children under 16, you could go to the same solicitor who arranged your separation but, if you want a fixed price, privacy and a quickie divorce, then go with me, a genuine Solicitor but one who offer the only online fixed price divorce available in Scotland.
With other solicitors you can pay anything from £1500-£3000 for this type of divorce. My firm is online and automated and offer a fixed price of £995. This includes VAT and all court costs.
There is lots of free information at MyScottishDivorce.co.uk so have a look at that.